483
483

May 3, 2020
05/20

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...

202
202

Mar 5, 2013
03/13

by
Bishnu Charan Sarkar, Saumen Chakraborty

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Nonlinear dynamics of a third order phase locked loop (PLL) using a resonant low pass filter in the face of continuous wave (CW) and frequency modulated (FM) input signals is examined. The role of design parameters of the loop resonant filter and the modulation index of the input FM signal on the system dynamics is studied numerically as well as experimentally. The occurrence of chaotic oscillations in the PLL is verified by evaluating some well-known chaos quantifiers like Lyapunov Exponents...

Topics: Third Order PLL, Resonant Filter, Stability Analysis, Chaotic dynamics, Lyapunov Exponent

Nonlinear dynamics of a third order phase locked loop (PLL) using a resonant low pass filter in the face of continuous wave (CW) and frequency modulated (FM) input signals is examined. The role of design parameters of the loop resonant filter and the modulation index of the input FM signal on the system dynamics is studied numerically as well as experimentally. The occurrence of chaotic oscillations in the PLL is verified by evaluating some well-known chaos quantifiers like Lyapunov Exponents...

Topics: Third Order PLL, Resonant Filter, Stability Analysis, Chaotic dynamics, Lyapunov Exponent.

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30

Jun 26, 2018
06/18

by
Jean-Marc Ginoux

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In 1908 Henri Poincar\'e gave a series of 'forgotten lectures' on wireless telegraphy in which he demonstrated the existence of a stable limit cycle in the phase plane. In 1929 Aleksandr Andronov published a short note in the Comptes Rendus in which he stated that there is a correspondence between the periodic solution of self-oscillating systems and the concept of stable limit cycles introduced by Poincar\'e. In this article Jean-Marc Ginoux describes these two major contributions to the...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1501.03282

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24

Jun 28, 2018
06/18

by
V. K. Chandrasekar; S. Karthiga; M. Lakshmanan

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The quenching of oscillations in interacting systems leads to several unwanted situations, which necessitate a suitable remedy to overcome the quenching. In this connection, this work addresses a mechanism that can resurrect oscillations in a typical situation. Through both numerical and analytical studies, we show the candidate which is capable of resurrecting oscillations is nothing but the feedback, the one which is profoundly used in dynamical control and in bio-therapies. Even in the case...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1506.05650

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...

19
19

Jun 26, 2018
06/18

by
Brian R. Hunt; Edward Ott

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In this paper we propose, discuss and illustrate a computationally feasible definition of chaos which can be applied very generally to situations that are commonly encountered, including attractors, repellers and non-periodically forced systems. This definition is based on an entropy-like quantity, which we call "expansion entropy", and we define chaos as occurring when this quantity is positive. We relate and compare expansion entropy to the well-known concept of topological entropy,...

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

Source: http://arxiv.org/abs/1501.07896

18
18

Jun 30, 2018
06/18

by
Simon Candelaresi; David Ian Pontin; Gunnar Hornig

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We present a simple method to efficiently compute a lower limit of the topological entropy for two-dimensional mappings. These mappings could represent either two-dimensional time-periodic fluid flows or three-dimensional magnetic fields, which are periodic in one direction. This method is based on measuring the length of a material line in the flow. Depending on the nature of the flow, the fluid can be mixed very efficiently which causes the line to stretch. Here we introduce a method to...

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

Source: http://arxiv.org/abs/1702.00441

18
18

Jun 27, 2018
06/18

by
Elizabeth Bradley; Holger Kantz

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In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space reconstruction, this set of methods allows us to compute characteristic quantities such as Lyapunov exponents and fractal dimensions, to predict the future course of the time series, and even to reconstruct the equations of motion in some cases. In practice,...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1503.07493

16
16

Jun 30, 2018
06/18

by
Moises Santillan

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We designed and developed a master-slave electronic oscillatory system (based on the 555-timer IC working in the astable mode), and investigated its dynamic behavior regarding synchronization. For that purpose we measured the rotation numbers corresponding to the phase-locking rhythms achieved in a large set of values of the normalized forcing frequency (NFF) and of the coupling strength between the master and the slave oscillators. In particular we were interested in the system behavior in the...

Topics: Nonlinear Sciences, Adaptation and Self-Organizing Systems, Chaotic Dynamics

Source: http://arxiv.org/abs/1407.6763

16
16

Jun 27, 2018
06/18

by
Tiberiu Harko; Chor Yin Ho; Chun Sing Leung; Stan Yip

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We perform the study of the stability of the Lorenz system by using the Jacobi stability analysis, or the Kosambi-Cartan-Chern (KCC) theory. The Lorenz model plays an important role for understanding hydrodynamic instabilities and the nature of the turbulence, also representing a non-trivial testing object for studying non-linear effects. The KCC theory represents a powerful mathematical method for the analysis of dynamical systems. In this approach we describe the evolution of the Lorenz...

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

Source: http://arxiv.org/abs/1504.02880

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15

Jun 28, 2018
06/18

by
Petr Braun

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The arithmetic triangular billiards are classically chaotic but have Poissonian energy level statistics, in ostensible violation of the BGS conjecture. We show that the length spectra of their periodic orbits divides into subspectra differing by the parity of the number of reflections from the triangle sides; in the quantum treatment that parity defines the reflection phase of the orbit contribution to the Gutzwiller formula for the energy level density. We apply these results to all 85...

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

Source: http://arxiv.org/abs/1508.02075

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14

Jun 27, 2018
06/18

by
Euaggelos E. Zotos

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The aim of this work is to review and also explore even further the escape properties of orbits in a dynamical system of a two-dimensional perturbed harmonic oscillator, which is a characteristic example of open Hamiltonian systems. In particular, we conduct a thorough numerical investigation distinguishing between trapped (ordered and chaotic) and escaping orbits, considering only unbounded motion for several energy levels. It is of particular interest, to locate the basins of escape towards...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1505.03847

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14

Jun 27, 2018
06/18

by
G. A. Leonov; N. V. Kuznetsov; T. N. Mokaev

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In this tutorial, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky--Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1505.04729

13
13

Jun 26, 2018
06/18

by
M Perin; C Chandre; P. J. Morrison; E Tassi

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Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are identified. Two Hamiltonian models emerge, for which the explicit closures are given, along with their Poisson brackets and Casimir invariants.

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

Source: http://arxiv.org/abs/1502.04639

13
13

Jun 27, 2018
06/18

by
Thanos Manos; Marko Robnik

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We review our recent works on the dynamical localization in the quantum kicked rotator (QKR) and the related properties of the classical kicked rotator (the standard map, SM). We introduce the Izrailev $N$-dimensional model of the QKR and analyze the localization properties of the Floquet eigenstates [{\em Phys. Rev. E} {\bf 87}, 062905 (2013)], and the statistical properties of the quasienergy spectra. We survey normal and anomalous diffusion in the SM, and the related accelerator modes [{\em...

Topics: Quantum Physics, Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1504.03022

13
13

Jun 29, 2018
06/18

by
Ezequiel Bianco-Martinez; Murilo S. Baptista

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In a causal world the direction of the time arrow dictates how past causal events in a variable $X$ produce future effects in $Y$. $X$ is said to cause an effect in $Y$, if the predictability (uncertainty) about the future states of $Y$ increases (decreases) as its own past and the past of $X$ are taken into consideration. Causality is thus intrinsic dependent on the observation of the past events of both variables involved, to the prediction (or uncertainty reduction) of future event of the...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.05023

13
13

Jun 28, 2018
06/18

by
N. V. Kuznetsov; O. A. Kuznetsova; G. A. Leonov; P. Neittaanmaki; M. V. Yuldashev; R. V. Yuldashev

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Nonlinear analysis of the classical phase-locked loop (PLL) is a challenging task. In classical engineering literature simplified mathematical models and simulation are widely used for its study. In this work the limitations of classical engineering phase-locked loop analysis are demonstrated, e.g., hidden oscillations, which can not be found by simulation, are discussed. It is shown that the use of simplified dynamical models and the application of simulation may lead to wrong conclusions...

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

Source: http://arxiv.org/abs/1507.03468

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12

Jun 27, 2018
06/18

by
M. Daniel Sweetlin; G. Sivaganesh

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In this paper we present numerical and analytical studies on the complete synchronization phenomena exhibited by unidirectionally coupled two variant of Murali-Lakshmanan-Chua circuits. The transition of the coupled system from an unsynchronized state to a state of complete synchronization under the influence of the coupling parameter is observed through phase portraits obtained numerically and analytically.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1505.01090

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11

Jun 28, 2018
06/18

by
Aminur Rahman; Denis Blackmore

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Logical RS flip-flop circuits are investigated once again in the context of discrete planar dynamical systems, but this time starting with simple bilinear (minimal) component models based on fundamental principles. The dynamics of the minimal model is described in detail, and shown to exhibit some of the expected properties, but not the chaotic regimes typically found in simulations of physical realizations of chaotic RS flip-flop circuits. Any physical realization of a chaotic logical circuit...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1507.03065

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10.0

Jun 26, 2018
06/18

by
S. V. Prants

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Dynamical systems theory approach has been successfully used in physical oceanography for the last two decades to study mixing and transport of water masses in the ocean. The basic theoretical ideas have been borrowed from the phenomenon of chaotic advection in fluids, an analogue of dynamical Hamiltonian chaos in mechanics. The starting point for analysis is a velocity field obtained by this or that way. Being motivated by successful applications of that approach to simplified analytic models...

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

Source: http://arxiv.org/abs/1502.01419

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10.0

Jun 28, 2018
06/18

by
V. Baladi; M. Todd

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We consider the one parameter family $\alpha \mapsto T_\alpha$ ($\alpha \in [0,1)$) of Pomeau-Manneville type interval maps $T_\alpha(x)=x(1+2^\alpha x^\alpha)$ for $x \in [0,1/2)$ and $T_\alpha(x)=2x-1$ for $x \in [1/2, 1]$, with the associated absolutely continuous invariant probability measure $\mu_\alpha$. For $\alpha \in (0,1)$, Sarig and Gou\"ezel proved that the system mixes only polynomially with rate $n^{1-1/\alpha}$ (in particular, there is no spectral gap). We show that for any...

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

Source: http://arxiv.org/abs/1508.02700

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10.0

Jun 30, 2018
06/18

by
Marek Czachor

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Arithmetic operations can be defined in various ways, even if one assumes commutativity and associativity of addition and multiplication, and distributivity of multiplication with respect to addition. In consequence, whenever one encounters `plus' or `times' one has certain freedom of interpreting this operation. This leads to some freedom in definitions of derivatives, integrals and, thus, practically all equations occurring in natural sciences. A change of realization of arithmetic, without...

Topics: Quantum Physics, Nonlinear Sciences, Chaotic Dynamics, Mathematics, General Relativity and Quantum...

Source: http://arxiv.org/abs/1412.8583

10
10.0

Jun 28, 2018
06/18

by
Buğçe Eminağa; Hatice Aktöre; Mustafa Riza

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This study introduces a modified quadratic Lorenz attractor. The properties of this new chaotic system are analysed and discussed in detail, by determining the equilibria points, the eigenvalues of the Jacobian, and the Lyapunov exponents. The numerical simulations, the time series analysis, and the projections to the $xy$-plane, $xz$-plane, and $yz$-plane are conducted to highlight the chaotic behaviour. The multiplicative form of the new system is also presented and the simulations are...

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

Source: http://arxiv.org/abs/1508.06840

10
10.0

Jun 26, 2018
06/18

by
M. Harsoula; G. Contopoulos; C. Efthymiopoulos

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We consider analytical formulae that describe the chaotic regions around the main periodic orbit $(x=y=0)$ of the H\'{e}non map. Following our previous paper (Efthymiopoulos, Contopoulos, Katsanikas $2014$) we introduce new variables $(\xi, \eta)$ in which the product $\xi\eta=c$ (constant) gives hyperbolic invariant curves. These hyperbolae are mapped by a canonical transformation $\Phi$ to the plane $(x,y)$, giving "Moser invariant curves". We find that the series $\Phi$ are...

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

Source: http://arxiv.org/abs/1502.00664

10
10.0

Jun 29, 2018
06/18

by
Cheng Xu; Chengqing Li; Jinhu Lü; Shi Shu

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This paper discusses the letter entitled "Network analysis of the state space of discrete dynamical systems" by A. Shreim et al. [Physical Review Letters, 98, 198701 (2007)]. We found that some theoretical analyses are wrong and the proposed indicators based on two parameters of the state-mapping network cannot discriminate the dynamical complexity of the discrete dynamical systems composed of a 1-D Cellular Automata.

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

Source: http://arxiv.org/abs/1611.06857

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10.0

Jun 27, 2018
06/18

by
O. Podvigina; V. Zheligovsky; U. Frisch

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A novel semi-Lagrangian method is introduced to solve numerically the Euler equation for ideal incompressible flow in arbitrary space dimension. It exploits the time-analyticity of fluid particle trajectories and requires, in principle, only limited spatial smoothness of the initial data. Efficient generation of high-order time-Taylor coefficients is made possible by a recurrence relation that follows from the Cauchy invariants formulation of the Euler equation (Zheligovsky & Frisch, J....

Topics: Nonlinear Sciences, Fluid Dynamics, Chaotic Dynamics, Numerical Analysis, Mathematics, Physics

Source: http://arxiv.org/abs/1504.05030

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10.0

Jun 26, 2018
06/18

by
Lei Wang; Xiao-Song Yang

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We revisit the famous Nos\'e-Hoover system in this paper and show the existence of some averagely conservative regions which are filled with an infinite sequence of nested tori. Depending on initial conditions, some invariant tori are of trefoil knot type, while the others are of trivial knot type. Moreover, we present a variety of interlinked invariant tori whose initial conditions are chosen from different averagely conservative regions and give all the interlinking numbers of those...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1501.03375

10
10.0

Jun 27, 2018
06/18

by
Quentin Aubourg; Nicolas Mordant

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We report a laboratory investigation of weak turbulence of water surface waves in the gravity-capillary crossover. By using time-space resolved profilometry and a bicoherence analysis, we observe that the nonlinear processes involve 3-wave resonant interactions. By studying the solutions of the resonance conditions we show that the nonlinear interaction is dominantly 1D and involves collinear wave vectors. Furthermore taking into account the spectral widening due to weak nonlinearity explains...

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

Source: http://arxiv.org/abs/1503.04110

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10.0

Jun 27, 2018
06/18

by
Juan Maldacena; Stephen H. Shenker; Douglas Stanford

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We conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent $\lambda_L \le 2 \pi k_B T/\hbar$. We give a precise mathematical argument, based on plausible physical...

Topics: Nonlinear Sciences, Condensed Matter, Quantum Physics, Chaotic Dynamics, Statistical Mechanics,...

Source: http://arxiv.org/abs/1503.01409

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10.0

Jun 28, 2018
06/18

by
M. Perin; Cristel Chandre; P. J. Morrison; E. Tassi

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Moment closures of the Vlasov-Amp{\`e}re system, whereby higher moments are represented as functions of lower moments with the constraint that the resulting fluid system remains Hamiltonian, are investigated by using water-bag theory. The link between the water-bag formalism and fluid models that involve density, fluid velocity, pressure and higher moments is established by introducing suitable thermodynamic variables. The cases of one, two and three water-bags are treated and their Hamiltonian...

Topics: Nonlinear Sciences, Statistical Mechanics, Physics, Condensed Matter, Chaotic Dynamics, Plasma...

Source: http://arxiv.org/abs/1507.02590

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10.0

Jun 27, 2018
06/18

by
Hanno Rein; Daniel Tamayo

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We present WHFast, a fast and accurate implementation of a Wisdom-Holman symplectic integrator for long-term orbit integrations of planetary systems. WHFast is significantly faster and conserves energy better than all other Wisdom-Holman integrators tested. We achieve this by significantly improving the Kepler-solver and ensuring numerical stability of coordinate transformations to and from Jacobi coordinates. These refinements allow us to remove the linear secular trend in the energy error...

Topics: Computational Physics, Nonlinear Sciences, Astrophysics, Physics, Chaotic Dynamics, Earth and...

Source: http://arxiv.org/abs/1506.01084

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10.0

Jun 27, 2018
06/18

by
Arindam Mishra; Chittaranjan Hens; Mridul Bose; Prodyot K. Roy; Syamal K. Dana

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We observe chimeralike states in an ensemble of oscillators using a type of global coupling consisting of two components: attractive and repulsive mean-field feedback. We identify existence of two types of chimeralike states in a bistable Li\'{e}nard system; in one type, both the coherent and the incoherent populations are in chaotic states (called as chaos-chaos chimeralike states) and, in another type, the incoherent population is in periodic state while the coherent population has irregular...

Topics: Chaotic Dynamics, Nonlinear Sciences, Adaptation and Self-Organizing Systems

Source: http://arxiv.org/abs/1506.00836

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Jun 27, 2018
06/18

by
Frank Hellmann; Paul Schultz; Carsten Grabow; Jobst Heitzig; Jürgen Kurths

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The notion of a part of phase space containing desired (or allowed) states of a dynamical system is important in a wide range of complex systems research. It has been called the safe operating space, the viability kernel or the sunny region. In this paper we define the notion of survivability: Given a random initial condition, what is the likelihood that the transient behaviour of a deterministic system does not leave a region of desirable states. We demonstrate the utility of this novel...

Topics: Chaotic Dynamics, Adaptation and Self-Organizing Systems, Nonlinear Sciences

Source: http://arxiv.org/abs/1506.01257

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9.0

Jun 26, 2018
06/18

by
Jean-Marc Ginoux

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The concept of "limit cycle" was introduced by Henri Poincar\'e in his second memoir "On curves defined by a differential equation" in 1882. From the point of view of physics, a stable limit cycle (or attractive) is the representation of the periodic solution of a (mechanical or electrical) dissipative system whose oscillations are maintained by the system itself. Conversely, the existence of a stable limit cycle ensures the maintenance of the oscillations. So far, the...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1501.03281

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9.0

Jun 27, 2018
06/18

by
G. Bianchi; N. V. Kuznetsov; G. A. Leonov; M. V. Yuldashev; R. V. Yuldashev

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Nonlinear analysis of the phase-locked loop (PLL) based circuits is a challenging task, thus in modern engineering literature simplified mathematical models and simulation are widely used for their study. In this work the limitations of numerical approach is discussed and it is shown that, e.g. hidden oscillations may not be found by simulation. Corresponding examples in SPICE and MatLab, which may lead to wrong conclusions concerning the operability of PLL-based circuits, are presented.

Topics: Other Computer Science, Nonlinear Sciences, Chaotic Dynamics, Dynamical Systems, Computing Research...

Source: http://arxiv.org/abs/1506.02484

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9.0

Jun 26, 2018
06/18

by
Z. Pouransari; L. Biferale; A. V. Johansson

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The concept of local isotropy in a chemically reacting turbulent wall-jet flow is addressed using direct numerical simulation (DNS) data. Different DNS databases with isothermal and exothermic reactions are examined. The chemical reaction and heat release effects on the turbulent velocity, passive scalar and reactive species fields are studied using their probability density functions (PDF) and higher order moments for velocities and scalar fields, as well as their gradients. With the aid of...

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

Source: http://arxiv.org/abs/1502.06113

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9.0

Jun 28, 2018
06/18

by
Ernest Montbrió; Diego Pazó; Alex Roxin

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A major goal of neuroscience, statistical physics and nonlinear dynamics is to understand how brain function arises from the collective dynamics of networks of spiking neurons. This challenge has been chiefly addressed through large-scale numerical simulations. Alternatively, researchers have formulated mean-field theories to gain insight into macroscopic states of large neuronal networks in terms of the collective firing activity of the neurons, or the firing rate. However, these theories have...

Topics: Quantitative Biology, Nonlinear Sciences, Neurons and Cognition, Adaptation and Self-Organizing...

Source: http://arxiv.org/abs/1506.06581

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9.0

Jun 28, 2018
06/18

by
G. A. Leonov; N. V. Kuznetsov; N. A. Korzhemanova; D. V. Kusakin

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The exact Lyapunov dimension formula for the Lorenz system has been analytically obtained first due to G.A.Leonov in 2002 under certain restrictions on parameters, permitting classical values. He used the construction technique of special Lyapunov-type functions developed by him in 1991 year. Later it was shown that the consideration of larger class of Lyapunov-type functions permits proving the validity of this formula for all parameters of the system such that all the equilibria of the system...

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

Source: http://arxiv.org/abs/1508.07498

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Jun 27, 2018
06/18

by
Robin Gutöhrlein; Jan Schnabel; Ibrokhim Iskandarov; Holger Cartarius; Jörg Main; Günter Wunner

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In open double-well Bose-Einstein condensate systems which balance in- and outfluxes of atoms and which are effectively described by a non-hermitian PT-symmetric Hamiltonian PT-symmetric states have been shown to exist. PT-symmetric states obey parity and time reversal symmetry. We tackle the question of how the in- and outfluxes can be realized and introduce a hermitian system in which two PT-symmetric subsystems are embedded. This system no longer requires an in- and outcoupling to and from...

Topics: Condensed Matter, Quantum Physics, Nonlinear Sciences, Quantum Gases, Chaotic Dynamics

Source: http://arxiv.org/abs/1503.01660

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Jun 27, 2018
06/18

by
Konstantin Batygin; Katherine M. Deck; Matthew J. Holman

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The GJ876 system was among the earliest multi-planetary detections outside of the Solar System, and has long been known to harbor a resonant pair of giant planets. Subsequent characterization of the system revealed the presence of an additional Neptune mass object on an external orbit, locked in a three body Laplace mean motion resonance with the previously known planets. While this system is currently the only known extrasolar example of a Laplace resonance, it differs from the Galilean...

Topics: Nonlinear Sciences, Chaotic Dynamics, Astrophysics, Mathematics, Dynamical Systems, Earth and...

Source: http://arxiv.org/abs/1504.00051

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Jun 26, 2018
06/18

by
A. P. Kuznetsov; L. V. Turukina; N. Yu. Chernyshov; Yu. V. Sedova

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Synchronization of forced reactively coupled van der Pol oscillators is investigated in the phase approximation. We discuss essential features of the reactive coupling. Bifurcation mechanisms for the destruction of complete synchronization and possible quasi-periodic regimes of different types are revealed. Regimes when autonomous oscillators demonstrate frequency locking and beating regimes with incommensurate frequencies are considered and compared.

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1502.03564

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Jun 26, 2018
06/18

by
Saverio E. Spagnolie; Colin Wahl; Joseph Lukasik; Jean-Luc Thiffeault

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Recent experiments and numerical simulations have shown that certain types of microorganisms "reflect" off of a flat surface at a critical angle of departure, independent of the angle of incidence. The nature of the reflection may be active (cell and flagellar contact with the surface) or passive (hydrodynamic) interactions. We explore the billiard-like motion of a body with this empirical reflection law inside a regular polygon and show that the dynamics can settle on a stable...

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

Source: http://arxiv.org/abs/1502.01478

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9.0

Jun 27, 2018
06/18

by
X. San Liang

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Information flow (or information transfer as may be called) the widely applicable general physics notion can be rigorously derived from first principles, rather than axiomatically proposed as an ansatz. Its logical association with causality and, particularly, the most stringent one-way causality, if existing, is firmly substantiated and stated as a fact in proved theorems. Established in this study are the information flows among the components of time-discrete mappings and time-continuous...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1503.08389

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8.0

Jun 26, 2018
06/18

by
Tal Kachman; Shmuel Fishman; Avy Soffer

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We consider the problem of numerically solving the Schr\"odinger equation with a potential that is quasi periodic in space and time. We introduce a numerical scheme based on a newly developed multi-time scale and averaging technique. We demonstrate that with this novel method we can solve efficiently and with rigorous control of the error such an equation for long times. A comparison with the standard split-step method shows substantial improvement in computation times, besides the...

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

Source: http://arxiv.org/abs/1501.03132

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8.0

Jun 28, 2018
06/18

by
Massimo Ostilli; Wagner Figueiredo

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We consider a simple model of communities interacting via bilinear terms. After analyzing the thermal equilibrium case, which can be described by an Hamiltonian, we introduce the dynamics that, for Ising-like variables, reduces to a Glauber-like dynamics. We analyze and compare four different versions of the dynamics: flow (differential equations), map (discrete-time dynamics), local-time update flow, and local-time update map. The presence of only bilinear interactions prevent the flow cases...

Topics: Chaotic Dynamics, Disordered Systems and Neural Networks, Statistical Mechanics, Nonlinear...

Source: http://arxiv.org/abs/1509.07405

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8.0

Jun 28, 2018
06/18

by
Lukas Gilz; Eike P. Thesing; James R. Anglin

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Even microscopic engines have hitherto been defined to require macroscopic elements such as heat reservoirs, but here we observe that what makes engines useful is energy transfer across a large ratio of dynamical time scales ("downconversion"), and that small, closed dynamical systems which could perform steady downconversion ("Hamiltonian daemons") would fulfill the practical requirements of autonomous microscopic engines. We show that such daemons are possible, and obey...

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

Source: http://arxiv.org/abs/1509.02778

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8.0

Jun 28, 2018
06/18

by
A. V. Makarenko

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A new approach is proposed to the analysis of generalized synchronization of multidimensional chaotic systems. The approach is based on the symbolic analysis of discrete sequences in the basis of a finite T-alphabet. In fact, the symbols of the T-alphabet encode the shape (the geometric structure) of a trajectory of a dynamical system. Investigation of symbolic sequences allows one to diagnose various regimes of chaos synchronization, including generalized synchronization. The characteristics...

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

Source: http://arxiv.org/abs/1507.03103

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8.0

Jun 28, 2018
06/18

by
Simona Olmi; Erik A. Martens; Shashi Thutupalli; Alessandro Torcini

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Two symmetrically coupled populations of N oscillators with inertia $m$ display chaotic solutions with broken symmetry similar to experimental observations with mechanical pendula. In particular, we report the first evidence of intermittent chaotic chimeras, where one population is synchronized and the other jumps erratically between laminar and turbulent phases. These states have finite life-times diverging as a power-law with N and m. Lyapunov analyses reveal chaotic properties in...

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

Source: http://arxiv.org/abs/1507.07685

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Jun 30, 2018
06/18

by
Seth D. Cohen

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We report on structures in a scale-dependent Lyapunov exponent of an experimental chaotic map that arise due to discontinuities in the map. The chaos is realized in an autonomous Boolean network which is constructed using asynchronous logic gates to form a map operator that outputs an unclocked pulse-train of varying widths. The map operator executes pulse-width stretching and folding and the operator's output is fed back to its input to continuously iterate the map. Using a simple model, we...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1412.1036