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264

May 3, 2020
05/20

May 3, 2020
by
R. Z. Sagdeev ( Ed.)

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This collection of articles by leading Soviet Scientists reflects the latest investigations dealing with turbulence transitions, the emergence of stochasticity, and the appearance of coherent structures in hydrodynamic-type systems and the theory of strong turbulence. Possible applications of these new approaches to hydrodynamics, plasma physics, astrophysics, the theory of chemical reactions, and biophysics are discussed. Intended for specialists in nonlinear, turbulent and stochastic...

Topics: mir books, mir publishers, physics, plasma, non linear dynamics, hydrodynamics, oscillating...

In the ocean, propagules with a planktonic stage are typically dispersed some distance downstream of the parent generation, introducing an asymmetry to the dispersal. Ocean-dwelling species have also been shown to exhibit chaotic population dynamics. Therefore, we must better understand chaotic population dynamics under the influence of asymmetrical dispersal. Here, we examine a density-dependent population in a current, where the current has both a mean and stochastic component. In our finite...

Topics: Asymmetric dispersal, Chaotic dynamics, Gaussian kernel dispersal, Logistic map, Spatial population...

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Jun 30, 2018
06/18

Jun 30, 2018
by
Chandrakala Meena; Pranay Deep Rungta; Sudeshna Sinha

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We explore Random Scale-Free networks of populations, modelled by chaotic Ricker maps, connected by transport that is triggered when population density in a patch is in excess of a critical threshold level. Our central result is that threshold-activated dispersal leads to stable fixed populations, for a wide range of threshold levels. Further, suppression of chaos is facilitated when the threshold-activated migration is more rapid than the intrinsic population dynamics of a patch. Additionally,...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.08506

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1.0

Jun 30, 2018
06/18

Jun 30, 2018
by
K. P. Harikrishnan; Rinku Jacob; R. Misra; G. Ambika

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The analysis of observed time series from nonlinear systems is usually done by making a time-delay reconstruction to unfold the dynamics on a multi-dimensional state space. An important aspect of the analysis is the choice of the correct embedding dimension. The conventional procedure used for this is either the method of false nearest neighbors or the saturation of some invariant measure, such as, correlation dimension. Here we examine this issue from a complex network perspective and propose...

Topics: Physics, Neurons and Cognition, Data Analysis, Statistics and Probability, Nonlinear Sciences,...

Source: http://arxiv.org/abs/1704.08585

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Jun 30, 2018
06/18

Jun 30, 2018
by
Maciej A. Nowak; Wojciech Tarnowski

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Using diagrammatic techniques, we provide an explicit proof of the single ring theorem, including the recent extension for the correlation function built out of left and right eigenvectors of a non-Hermitian matrix. We present the operational formalism allowing to map mutually the two distinct areas of free random variables: Hermitian positive definite operators and non-normal R-diagonal operators, realized as the large size limit of biunitarily invariant random matrices.

Topics: Operator Algebras, Mathematical Physics, Nonlinear Sciences, Combinatorics, Chaotic Dynamics,...

Source: http://arxiv.org/abs/1704.07719

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Jun 30, 2018
06/18

Jun 30, 2018
by
Juan M. Restrepo

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A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically update the likelihood with the aim of making better use of low uncertainty sparse observations. The filter is applied to a problem with linear dynamics and Gaussian statistics, and compared to the exact estimate, a model outcome, and the Kalman filter...

Topics: Dynamical Systems, Chaotic Dynamics, Nonlinear Sciences, Mathematics

Source: http://arxiv.org/abs/1704.07435

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Jun 30, 2018
06/18

Jun 30, 2018
by
Marat Akhmet; Mehmet Onur Fen

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To make research of chaos more friendly with discrete equations, we introduce the concept of an unpredictable sequence as a specific unpredictable function on the set of integers. It is convenient to be verified as a solution of a discrete equation. This is rigorously proved in this paper for quasilinear systems, and we demonstrate the result numerically for linear systems in the critical case with respect to the stability of the origin. The completed research contributes to the theory of chaos...

Topics: Chaotic Dynamics, Nonlinear Sciences, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1704.06963

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2.0

Jun 30, 2018
06/18

Jun 30, 2018
by
Marat Akhmet; Mehmet Onur Fen

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Periodicity plays a significant role in the chaos theory from the beginning since the skeleton of chaos can consist of infinitely many unstable periodic motions. This is true for chaos in the sense of Devaney [1], Li-Yorke [2] and the one obtained through period-doubling cascade [3]. Countable number of periodic orbits exist in any neighborhood of a structurally stable Poincar\'{e} homoclinic orbit, which can be considered as a criterion for the presence of complex dynamics [4]-[6]. It was...

Topics: Chaotic Dynamics, Nonlinear Sciences, Dynamical Systems, Mathematics

Source: http://arxiv.org/abs/1704.06854

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Jun 30, 2018
06/18

Jun 30, 2018
by
Lucas Lacasa; Wolfram Just

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Visibility algorithms are a family of geometric and ordering criteria by which a real-valued time series of N data is mapped into a graph of N nodes. This graph has been shown to often inherit in its topology non-trivial properties of the series structure, and can thus be seen as a combinatorial representation of a dynamical system. Here we explore in some detail the relation between visibility graphs and symbolic dynamics. To do that, we consider the degree sequence of horizontal visibility...

Topics: Physics, Data Analysis, Statistics and Probability, Nonlinear Sciences, Dynamical Systems, Chaotic...

Source: http://arxiv.org/abs/1704.06467

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Jun 30, 2018
06/18

Jun 30, 2018
by
M. J. Olascoaga; F. J. Beron-Vera; Y. Wang; J. Triñanes; P. Pérez-Brunius

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Ocean flows are routinely inferred from low-resolution satellite altimetry measurements of sea surface height (SSH) assuming a geostrophic balance. Recent nonlinear dynamical systems techniques have revealed that altimetry-inferred flows can support mesoscale eddies with material boundaries that do not filament for many months, thereby representing effective mechanisms for coherent transport. However, the significance of such coherent Lagrangian eddies is not free from uncertainty due to the...

Topics: Fluid Dynamics, Physics, Chaotic Dynamics, Nonlinear Sciences, Atmospheric and Oceanic Physics

Source: http://arxiv.org/abs/1704.06186

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Jun 30, 2018
06/18

Jun 30, 2018
by
Chiranjit Mitra; Tim Kittel; Anshul Choudhary; Jürgen Kurths; Reik V. Donner

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Maintaining the synchronous motion of dynamical systems interacting on complex networks is often critical to their functionality. However, real-world networked dynamical systems operating synchronously are prone to random perturbations driving the system to arbitrary states within the corresponding basin of attraction, thereby leading to epochs of desynchronized dynamics with a priori unknown durations. Thus, it is highly relevant to have an estimate of the duration of such transient phases...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.06079

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Jun 30, 2018
06/18

Jun 30, 2018
by
G. O. Agaba; Y. N. Kyrychko; K. B. Blyuss

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This paper analyses the dynamics of infectious disease with a concurrent spread of disease awareness. The model includes local awareness due to contacts with aware individuals, as well as global awareness due to reported cases of infection and awareness campaigns. We investigate the effects of time delay in response of unaware individuals to available information on the epidemic dynamics by establishing conditions for the Hopf bifurcation of the endemic steady state of the model. Analytical...

Topics: Populations and Evolution, Quantitative Biology, Chaotic Dynamics, Nonlinear Sciences, Quantitative...

Source: http://arxiv.org/abs/1704.05912

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Jun 30, 2018
06/18

Jun 30, 2018
by
Guglielmo Lacorata; Angelo Vulpiani

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A deterministic multi-scale dynamical system is introduced and discussed as prototype model for relative dispersion in stationary, homogeneous and isotropic turbulence. Unlike stochastic diffusion models, here trajectory transport and mixing properties are entirely controlled by Lagrangian Chaos. The anomalous "sweeping effect", a known drawback common to kinematic simulations, is removed thanks to the use of quasi-Lagrangian coordinates. Lagrangian dispersion statistics of the model...

Topics: Fluid Dynamics, Physics, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.05372

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Jun 30, 2018
06/18

Jun 30, 2018
by
Kushal Shah; Dmitry Turaev; Vassili Gelfreich; Vered Rom-Kedar

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Ergodicity is a fundamental requirement for a dynamical system to reach a state of statistical equilibrium. On the other hand, it is known that in slow-fast systems ergodicity of the fast sub- system impedes the equilibration of the whole system due to the presence of adiabatic invariants. Here, we show that the violation of ergodicity in the fast dynamics effectively drives the whole system to equilibrium. To demonstrate this principle we investigate dynamics of the so-called springy...

Topics: Dynamical Systems, Chaotic Dynamics, Nonlinear Sciences, Mathematics

Source: http://arxiv.org/abs/1704.04954

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1.0

Jun 30, 2018
06/18

Jun 30, 2018
by
S. E. Marzen; J. P. Crutchfield

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Loosely speaking, the Shannon entropy rate is used to gauge a stochastic process' intrinsic randomness; the statistical complexity gives the cost of predicting the process. We calculate, for the first time, the entropy rate and statistical complexity of stochastic processes generated by finite unifilar hidden semi-Markov models---memoryful, state-dependent versions of renewal processes. Calculating these quantities requires introducing novel mathematical objects ({\epsilon}-machines of hidden...

Topics: Condensed Matter, Statistics Theory, Computing Research Repository, Nonlinear Sciences, Statistical...

Source: http://arxiv.org/abs/1704.04707

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Jun 30, 2018
06/18

Jun 30, 2018
by
Hai-Lin Zou; Zi-Chen Deng; Wei-Peng Hu; Kazuyuki Aihara; Ying-Cheng Lai

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The asymptotic attractors of a nonlinear dynamical system play a key role in the long-term physically observable behaviors of the system. The study of attractors and the search for distinct types of attractor have been a central task in nonlinear dynamics. In smooth dynamical systems, an attractor is often enclosed completely in its basin of attraction with a finite distance from the basin boundary. Recent works have uncovered that, in neuronal networks, unstable attractors with a remote basin...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.04185

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0.0

Jun 30, 2018
06/18

Jun 30, 2018
by
O. González-Gaxiola; G. Chacón Acosta; J. A. Santiago García

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In this paper, He's frequency-amplitude formulation with some choice of location points that improve accuracy is applied to determine the periodic solution for the nonlinear oscillations of a punctual charge in the electric field of charged ring. The results of the present study are valid for small and large amplitudes of oscillation. The present method can be applied directly to highly nonlinear problems without any discretization, linearization or restrictive assumptions. Finally, compared...

Topics: Physics, Chaotic Dynamics, Nonlinear Sciences, Classical Physics

Source: http://arxiv.org/abs/1704.04107

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Jun 30, 2018
06/18

Jun 30, 2018
by
A. Aliakbari; P. Manshour; M. J. Salehi

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The records statistics in stationary and non-stationary fractal time series is studied extensively. By calculating various concepts in record dynamics, we find some interesting results. In stationary fractional Gaussian noises, we observe a universal behavior for the whole range of Hurst exponents. However, for non-stationary fractional Brownian motions the record dynamics is crucially dependent on the memory, which plays the role of a non-stationarity index, here. Indeed, the deviation from...

Topics: Physics, Data Analysis, Statistics and Probability, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.04377

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0.0

Jun 30, 2018
06/18

Jun 30, 2018
by
Euaggelos E. Zotos

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The Copenhagen problem where the primaries of equal masses are magnetic dipoles is used in order to determine the Newton-Raphson basins of attraction associated with the equilibrium points. The parametric variation of the position as well as of the stability of the Lagrange points are monitored when the value of the ratio $\lambda$ of the magnetic moments varies in predefined intervals. The regions on the configuration $(x,y)$ plane occupied by the basins of convergence are revealed using the...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.02273

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Jun 30, 2018
06/18

Jun 30, 2018
by
Patrick J. Blonigan; Qiqi Wang

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Sensitivity analysis methods are important tools for research and design with simulations. Many important simulations exhibit chaotic dynamics, including scale-resolving turbulent fluid flow simulations. Unfortunately, conventional sensitivity analysis methods are unable to compute useful gradient information for long-time-averaged quantities in chaotic dynamical systems. Sensitivity analysis with least squares shadowing (LSS) can compute useful gradient information for a number of chaotic...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.02047

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Jun 30, 2018
06/18

Jun 30, 2018
by
L. P Horwitz; D. Zucker

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We study classically the problem of two relativistic particles with an invariant Duffing-like potential which reduces to the usual Duffing form in the nonrelativistic limit. We use a special relativistic generalization (RGEM) of the geometric method (GEM) developed for the analysis of nonrelativistic Hamiltonian systems to study the local stability of a relativistic Duffing oscillator. Poincar'e plots of the simulated motion are consistent with the RGEM. We found a threshold for the external...

Topics: Physics, Mathematical Physics, Nonlinear Sciences, Classical Physics, Chaotic Dynamics, Mathematics

Source: http://arxiv.org/abs/1704.00811

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Jun 30, 2018
06/18

Jun 30, 2018
by
A. Ishaq Ahamed; M. Lakshmanan

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We report using Clarke's concept of generalised differential and a modification of Floquet theory to non-smooth oscillations, the occurrence of discontinuity induced Hopf bifurcations and Neimark-Sacker bifurcations leading to quasiperiodic attractors in a memristive Murali-Lakshmanan-Chua (memristive MLC) circuit. The above bifurcations arise because of the fact that a memristive MLC circuit is basically a nonsmooth system by virtue of having a memristive element as its nonlinearity. The...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.01167

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Jun 30, 2018
06/18

Jun 30, 2018
by
A. Berera; R. D. J. G. Ho

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By tracking the divergence of two initially close trajectories in phase space of forced turbulence, the relation between the maximal Lyapunov exponent $\lambda$, and the Reynolds number $Re$ is measured using direct numerical simulations, performed on up to $2048^3$ collocation points. The Lyapunov exponent is found to solely depend on the Reynolds number with $\lambda \propto Re^{0.53}$ and that after a transient period the divergence of trajectories grows at the same rate at all scales....

Topics: Fluid Dynamics, Physics, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1704.01042

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Jun 30, 2018
06/18

Jun 30, 2018
by
Vladimir García-Morales

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It is shown that characteristic functions of classical `crisp' sets can be made fuzzy by means of a $\mathcal{B}_{\kappa}$-function that we have recently introduced, and where the fuzziness parameter $\kappa \in \mathbb{R}$ controls how much a fuzzy set deviates from the crisp set obtained in the limit $\kappa \to 0$. A theorem is established that yields novel expressions for the union, negation, and intersection of both classical and fuzzy sets. As an application, we establish a theorem on the...

Topics: Chaotic Dynamics, Nonlinear Sciences, Mathematical Physics, Mathematics

Source: http://arxiv.org/abs/1704.00676

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Jun 30, 2018
06/18

Jun 30, 2018
by
Viviane Baladi

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We show that characteristic functions of domains with boundaries transversal to stable cones are bounded multipliers on a recently introduced scale U^{t,s}_p of anisotropic Banach spaces, under the conditions -1+1/p

Topics: Nonlinear Sciences, Dynamical Systems, Functional Analysis, Chaotic Dynamics, Mathematics

Source: http://arxiv.org/abs/1704.00157

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Jun 30, 2018
06/18

Jun 30, 2018
by
Dongmei Song; Yafeng Wang; Xiang Gao; Shi-Xian Qu; Ying-Cheng Lai; Xingang Wang

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Dynamical patterns in complex networks of coupled oscillators are both of theoretical and practical interest, yet to fully reveal and understand the interplay between pattern emergence and network structure remains to be an outstanding problem. A fundamental issue is the effect of network structure on the stability of the patterns. We address this issue by using the setting where random links are systematically added to a regular lattice and focusing on the dynamical evolution of spiral wave...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.10952

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Jun 30, 2018
06/18

Jun 30, 2018
by
Varun Pandit; Archan Mukhopadhyay; Sagar Chakraborty

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Replicator equation---a paradigm equation in evolutionary game dynamics---mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players, interaction is modeled by a two-strategy symmetric...

Topics: Physics, Chaotic Dynamics, Nonlinear Sciences, Biological Physics

Source: http://arxiv.org/abs/1703.10767

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Jun 30, 2018
06/18

Jun 30, 2018
by
Nazmi Burak Budanur; Björn Hof

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In shear flows at transitional Reynolds numbers, localized patches of turbulence, known as puffs, coexist with the laminar flow. Recently, Avila et al., Phys. Rev. Let. 110, 224502 (2013) discovered two spatially localized relative periodic solutions for pipe flow, which appeared in a saddle-node bifurcation at low speeds. Combining slicing methods for continuous symmetry reduction with Poincar\'e sections for the first time in a shear flow setting, we compute and visualize the unstable...

Topics: Pattern Formation and Solitons, Fluid Dynamics, Physics, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.10484

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Jun 30, 2018
06/18

Jun 30, 2018
by
M. A. Kiseleva; E. V. Kudryashova; N. V. Kuznetsov; O. A. Kuznetsova; G. A. Leonov; M. V. Yuldashev; R. V. Yuldashev

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Nowadays various chaotic secure communication systems based on synchronization of chaotic circuits are widely studied. To achieve synchronization, the control signal proportional to the difference between the circuits signals, adjust the state of one circuit. In this paper the synchronization of two Chua circuits is simulated in SPICE. It is shown that the choice of control signal is be not straightforward, especially in the case of multistability and hidden attractors.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.09884

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Jun 30, 2018
06/18

Jun 30, 2018
by
Koji Hashimoto; Keiju Murata; Ryosuke Yoshii

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The out-of-time-order correlator (OTOC) is considered as a measure of quantum chaos. We formulate how to calculate the OTOC for quantum mechanics with a general Hamiltonian. We demonstrate explicit calculations of OTOCs for a harmonic oscillator, a particle in a one-dimensional box, a circle billiard and stadium billiards. For the first two cases, OTOCs are periodic in time because of their commensurable energy spectra. For the circle and stadium billiards, they are not recursive but saturate...

Topics: Condensed Matter, Disordered Systems and Neural Networks, Nonlinear Sciences, High Energy Physics -...

Source: http://arxiv.org/abs/1703.09435

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Jun 30, 2018
06/18

Jun 30, 2018
by
Mitsuyoshi Tomiya; Shoichi Sakamoto; Eric J. Heller

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This study analyzed the scar-like localization in the time-average of a timeevolving wavepacket on the desymmetrized stadium billiard. When a wavepacket is launched along the orbits, it emerges on classical unstable periodic orbits as a scar in the stationary states. This localization along the periodic orbit is clarified through the semiclassical approximation. It essentially originates from the same mechanism of a scar in stationary states: the piling up of the contribution from the classical...

Topics: Quantum Physics, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.08613

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Jun 30, 2018
06/18

Jun 30, 2018
by
Jing Zhang; Yizhen Yu; Xingang Wang

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Coupled metronomes serve as a paradigmatic model for exploring the collective behaviors of complex dynamical systems, as well as a classical setup for classroom demonstrations of synchronization phenomena. Whereas previous studies of metronome synchronization have been concentrating on symmetric coupling schemes, here we consider the asymmetric case by adopting the scheme of layered metronomes. Specifically, we place two metronomes on each layer, and couple two layers by placing one on top of...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.07936

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4.0

Jun 30, 2018
06/18

Jun 30, 2018
by
Deniz Eroglu; Jeroen Lamb; Tiago Pereira

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Dynamical networks are important models for the behaviour of complex systems, modelling physical, biological and societal systems, including the brain, food webs, epidemic disease in populations, power grids and many other. Such dynamical networks can exhibit behaviour in which deterministic chaos, exhibiting unpredictability and disorder, coexists with synchronization, a classical paradigm of order. We survey the main theory behind complete, generalized and phase synchronization phenomena in...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.08296

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Jun 30, 2018
06/18

Jun 30, 2018
by
G. P. Suarez; Miguel Hoyuelos; Dante R. Chialvo

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The study of fluctuation-induced transport is concerned with the directed motion of particles on a substrate when subjected to a fluctuating external field. Work over the last two decades provides now precise clues on how the average transport depends on three fundamental aspects: the shape of the substrate, the correlations of the fluctuations and the mass, geometry, interaction and density of the particles. These three aspects, reviewed here, acquire additional relevance because the same...

Topics: Condensed Matter, Chaotic Dynamics, Nonlinear Sciences, Soft Condensed Matter

Source: http://arxiv.org/abs/1703.07882

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1.0

Jun 30, 2018
06/18

Jun 30, 2018
by
François Gay-Balmaz; Darryl D. Holm

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Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's "Global Drifter Program", this paper develops data-driven stochastic models of geophysical fluid dynamics (GFD) with non-stationary spatial correlations representing the dynamical behaviour of oceanic currents. Three models are considered. Model 1 from \cite{Ho2015} is reviewed, in which the spatial...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.06774

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Jun 30, 2018
06/18

Jun 30, 2018
by
Andrzej J. Maciejewski; Wojciech Szumiński

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Two versions of the semi-classical Jaynes--Cummings model without the rotating wave approximation are investigated. It is shown that for a non-zero value of the coupling constant the version introduced by Belobrov, Zaslavsky, and Tartakovsky is Hamiltonian with respect to a certain degenerated Poisson bracket. Moreover, it is shown that both models are not integrable.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.06625

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Jun 30, 2018
06/18

Jun 30, 2018
by
Wojciech Szumiński

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In this paper we consider Huang--Li nonlinear financial system recently studied in the literature. It has the form of three first order differential equations \[ \dot x=z+(y-a)x,\quad \dot y=1-b y-x^2,\quad \dot z=-x-c z, \] where $(a,b,c)$ are real positive parameters. We show that this system is not integrable in the class of functions meromorphic in variables $(x,y,z)$. We give an analytic proof of this fact analysing properties the of differential Galois group of variational equations along...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.06623

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Jun 30, 2018
06/18

Jun 30, 2018
by
Vladimir Klinshov; Serhiy Yanchuk; Artur Stephan; Vladimir Nekorkin

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Phase response curve (PRC) is an extremely useful tool for studying the response of oscillatory systems, e.g. neurons, to sparse or weak stimulation. Here we develop a framework for studying the response to a series of pulses which are frequent or/and strong so that the standard PRC fails. We show that in this case, the phase shift caused by each pulse depends on the history of several previous pulses. We call the corresponding function which measures this shift the phase response function...

Topics: Physics, Data Analysis, Statistics and Probability, Chaotic Dynamics, Nonlinear Sciences,...

Source: http://arxiv.org/abs/1703.05611

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Jun 30, 2018
06/18

Jun 30, 2018
by
Vincent Mourik; Serwan Asaad; Hannes Firgau; Jarryd J. Pla; Catherine Holmes; Gerard J. Milburn; Jeffrey C. McCallum; Andrea Morello

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Among the many controversial aspects of the quantum / classical boundary, the emergence of chaos remains amongst the least experimentally verified. In particular, the time-resolved observation of quantum chaotic dynamics, and its interplay with quantum measurement, is largely unexplored outside experiments in atomic ensembles. We present here a realistic proposal to construct a chaotic driven top from the nuclear spin of a single donor atom in silicon, in the presence of nuclear quadrupole...

Topics: Mesoscale and Nanoscale Physics, Quantum Physics, Condensed Matter, Chaotic Dynamics, Nonlinear...

Source: http://arxiv.org/abs/1703.04852

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Jun 30, 2018
06/18

Jun 30, 2018
by
Stéphane Vannitsem

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The deterministic equations describing the dynamics of the atmosphere (and of the climate system) are known to display the property of sensitivity to initial conditions. In the ergodic theory of chaos this property is usually quantified by computing the Lyapunov exponents. In this review, these quantifiers computed in a hierarchy of atmospheric models (coupled or not to an ocean) are analyzed, together with their local counterparts known as the local or finite-time Lyapunov exponents. It is...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.04284

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3.0

Jun 30, 2018
06/18

Jun 30, 2018
by
Jean-Regis Angilella; Daniel J. Case; Adilson E. Motter

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In the fluid transport of particles, it is generally expected that heavy particles carried by a laminar fluid flow moving downward will also move downward. We establish a theory to show, however, that particles can be dynamically levitated and lifted by interacting vortices in such flows, thereby moving against gravity and the asymptotic direction of the flow, even when they are orders of magnitude denser than the fluid. The particle levitation is rigorously demonstrated for potential flows and...

Topics: Fluid Dynamics, Physics, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.03296

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Jun 30, 2018
06/18

Jun 30, 2018
by
Shobhit Jain; Paolo Tiso; George Haller

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We apply two recently formulated mathematical techniques, Slow-Fast Decomposition (SFD) and Spectral Submanifold (SSM) reduction, to a von Karman beam with geometric nonlinearities and viscoelastic damping. SFD identifies a global slow manifold in the full system which attracts solutions at rates faster than typical rates within the manifold. An SSM, the smoothest nonlinear continuation of a linear modal subspace, is then used to further reduce the beam equations within the slow manifold. This...

Topics: Physics, Computational Engineering, Finance, and Science, Nonlinear Sciences, Computing Research...

Source: http://arxiv.org/abs/1703.03001

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Jun 30, 2018
06/18

Jun 30, 2018
by
Martin Rosalie

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Templates can be used to describe the topological properties of chaotic attractors. For attractors bounded by genus one torus, these templates are described by a linking matrix. For a given attractor, it has been shown that the template depends on the Poincar\'e section chosen to performed the analysis. The purpose of this article is to present an algorithm that gives the elementary mixer of a template in order to have a unique way to describe a chaotic mechanism. This chaotic mechanism is...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.02768

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Jun 30, 2018
06/18

Jun 30, 2018
by
Stephen C Creagh; Gabriele Gradoni; Timo Hartmann; Gregor Tanner

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We describe a novel approach for computing wave correlation functions inside finite spatial domains driven by complex and statistical sources. By exploiting semiclassical approximations, we provide explicit algorithms to calculate the local mean of these correlation functions in terms of the underlying classical dynamics. By defining appropriate ensemble averages, we show that fluctuations about the mean can be characterised in terms of classical correlations. We give in particular an explicit...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.02561

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Jun 30, 2018
06/18

Jun 30, 2018
by
Andrej Junginger; Jörg Main; Günter Wunner; Rigoberto Hernandez

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The complexity of arbitrary dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit - in the form of a limit cycle, dividing surface, instanton trajectories or some other related structure - can be uncovered. Determining such a periodic orbit, no matter how beguilingly simple it appears, is often very challenging. We present a method for the direct construction of unstable periodic orbits and instanton trajectories at saddle points...

Topics: Physics, Chaotic Dynamics, Nonlinear Sciences, Chemical Physics

Source: http://arxiv.org/abs/1703.02472

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Jun 30, 2018
06/18

Jun 30, 2018
by
Diego Garlaschelli; Frank den Hollander; Janusz Meylahn; Benthen Zeegers

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Synchronization of neurons forming a network with a hierarchical structure is essential for the brain to be able to function optimally. In this paper we study synchronization of phase oscillators on the most basic example of such a network, namely, the hierarchical lattice. Each oscillator has a natural frequency, drawn independently from a common probability distribution. In addition, pairs of oscillators interact with each other at a strength that depends on their hierarchical distance,...

Topics: Disordered Systems and Neural Networks, Condensed Matter, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.02535

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Jun 30, 2018
06/18

Jun 30, 2018
by
Massimiliano Di Ventra; Fabio L. Traversa

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Digital memcomputing machines (DMMs) are non-linear dynamical systems designed so that their equilibrium points are solutions of the Boolean problem they solve. In a previous work [Chaos 27, 023107 (2017)] it was argued that when DMMs support solutions of the associated Boolean problem then strange attractors cannot coexist with such equilibria. In this work, we demonstrate such conjecture. In particular, we show that both topological transitivity and the strongest property of topological...

Topics: Emerging Technologies, Chaotic Dynamics, Nonlinear Sciences, Computing Research Repository,...

Source: http://arxiv.org/abs/1703.02644

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Jun 30, 2018
06/18

Jun 30, 2018
by
Igor Franovic; Oleg V. Maslennikov; Iva Bacic; Vladimir I. Nekorkin

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We analyze the emergent regimes and the stimulus-response relationship of a population of noisy map neurons by means of a mean-field model, derived within the framework of cumulant approach complemented by the Gaussian closure hypothesis. It is demonstrated that the mean-field model can qualitatively account for stability and bifurcations of the exact system, capturing all the generic forms of collective behavior, including macroscopic excitability, subthreshold oscillations, periodic or...

Topics: Disordered Systems and Neural Networks, Chaotic Dynamics, Nonlinear Sciences, Condensed Matter,...

Source: http://arxiv.org/abs/1703.01964

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Jun 30, 2018
06/18

Jun 30, 2018
by
Pavel V. Kuptsov; Anna V. Kuptsova

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We consider extended starlike networks where the hub node is coupled with several chains of nodes representing star rays. Assuming that nodes of the network are occupied by nonidentical self-oscillators we study various forms of their cluster synchronization. Radial cluster emerges when the nodes are synchronized along a ray, while circular cluster is formed by nodes without immediate connections but located on identical distances to the hub. By its nature the circular synchronization is a new...

Topics: Networking and Internet Architecture, Chaotic Dynamics, Nonlinear Sciences, Computing Research...

Source: http://arxiv.org/abs/1703.01914

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Jun 30, 2018
06/18

Jun 30, 2018
by
William Graham Hoover; Carol Griswold Hoover

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The time-averaged Lyapunov exponents support a mechanistic description of the chaos generated in and by nonlinear dynamical systems. The exponents are ordered from largest to smallest with the largest one describing the exponential growth rate of the (small) distance between two neighboring phase-space trajectories. Two exponents describe the rate for areas defined by three nearby trajectories. The sum of the first three exponents is the rate for volumes defined by four nearby trajectories, and...

Topics: Statistical Mechanics, Condensed Matter, Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1703.00470