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0.0

Jun 29, 2018
06/18

by
Bidesh K. Bera; Chittaranjan Hens; Sourav K. Bhowmick; Pinaki Pal; Dibakar Ghosh

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We report a transition from homogeneous steady state to inhomogeneous steady state in coupled oscillators, both limit cycle and chaotic, under cyclic coupling and diffusive coupling as well when an asymmetry is introduced in terms of a negative parameter mismatch. Such a transition appears in limit cycle systems via pitchfork bifurcation as usual. Especially, when we focus on chaotic systems, the transition follows a transcritical bifurcation for cyclic coupling while it is a pitchfork...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1604.07943

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7.0

Jun 28, 2018
06/18

by
Lydia Bouchara; Ouerdia Ourrad; Sandro Vaienti; Xavier Leoncini

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The distribution of finite time observable averages and transport in low dimensional Hamiltonian systems is studied. Finite time observable average distributions are computed, from which an exponent $\alpha$ characteristic of how the maximum of the distributions scales with time is extracted. To link this exponent to transport properties, the characteristic exponent $\mu(q)$ of the time evolution of the different moments of order $q$ related to transport are computed. As a testbed for our study...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1509.00798

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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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0.0

Jun 29, 2018
06/18

by
Bidesh K. Bera; Dibakar Ghosh; Tanmoy Banerjee

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In this paper we report the occurrence of chimera patterns in a network of neuronal oscillators, which are coupled through {\it local}, synaptic {\it gradient} coupling. We discover a new chimera pattern, namely the {\it imperfect traveling chimera} where the incoherent traveling domain spreads into the coherent domain of the network. Remarkably, we also find that chimera states arise even for {\it one-way} local coupling, which is in contrast to the earlier belief that only nonlocal, global or...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1604.07936

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4.0

Jun 28, 2018
06/18

by
Bidesh K. Bera; Dibakar Ghosh; M. Lakshmanan

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We study the existence of chimera states in pulse-coupled networks of bursting Hindmarsh-Rose neurons with nonlocal, global and local (nearest neighbor) couplings. Through a linear stability analysis, we discuss the behavior of stability function in the incoherent (i.e. disorder), coherent, chimera and multi-chimera states. Surprisingly, we find that chimera and multi-chimera states occur even using local nearest neighbor interaction in a network of identical bursting neurons alone. This is in...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1507.02371

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0.0

Jun 29, 2018
06/18

by
Torleif Ericson; Barbara Dietz; Achim Richter

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Exact analytical expressions for the cross-section correlation functions of chaotic scattering sys- tems have hitherto been derived only under special conditions. The objective of the present article is to provide expressions that are applicable beyond these restrictions. The derivation is based on a statistical model of Breit-Wigner type for chaotic scattering amplitudes which has been shown to describe the exact analytical results for the scattering (S)-matrix correlation functions...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1605.07217

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0.0

Jun 29, 2018
06/18

by
Bastian Pietras; Andreas Daffertshofer

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The Ott-Antonsen (OA) ansatz [Chaos 18, 037113 (2008), Chaos 19, 023117 (2009)] has been widely used to describe large systems of coupled phase oscillators. If the coupling is sinusoidal and if the phase dynamics does not depend on the specific oscillator, then the macroscopic behavior of the systems can be fully described by a low-dimensional dynamics. Does the corresponding manifold remain attractive when introducing an intrinsic dependence between an oscillator's phase and its dynamics by...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1608.02723

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0.0

Jun 30, 2018
06/18

by
Z. Liu; M. Ouali; S. Coulibaly; M. G. Clerc; M. Taki; M. Tlidi

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Complex spatiotemporal dynamics have been a subject of recent experimental investigations in optical frequency comb microresonators and in driven fiber cavities with a Kerr-type media. We show that this complex behavior has a spatiotemporal chaotic nature. We determine numerically the Lyapunov spectra, allowing to characterize different dynamical behavior occurring in these simple devices. The Yorke-Kaplan dimension is used as an order parameter to characterize the bifurcation diagram. We...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1701.06023

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2.0

Jun 30, 2018
06/18

by
R. Jothimurugan; K. Suresh; P. Megavarna Ezhilarasu; K. Thamilmaran

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In this paper, we report an improved implementation of an inductorless third order autonomous canonical Chua's circuit. The active elements as well as the synthetic inductor employed in this circuit are designed using current feedback operational amplifiers (CFOAs). The reason for employing CFOAs is that they have better features such as high slew rate, high speed of operation, etc., which enable the circuit to operate at higher frequency ranges, when compared to the circuits designed using...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1408.4922

0
0.0

Jun 29, 2018
06/18

by
Vladimir García-Morales

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A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1601.03017

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0.0

Jun 29, 2018
06/18

by
Sudhanshu Shekhar Chaurasia; Sudeshna Sinha

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We explore the behaviour of an ensemble of chaotic oscillators coupled only to an external chaotic system, whose intrinsic dynamics may be similar or dissimilar to the group. Counter-intuitively, we find that a dissimilar external system manages to suppress the intrinsic chaos of the oscillators to fixed point dynamics, at sufficiently high coupling strengths. So, while synchronization is induced readily by coupling to an identical external system, control to fixed states is achieved only if...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1607.00462

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0.0

Jun 30, 2018
06/18

by
Will Cousins; Themistoklis P. Sapsis

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The aim of this work is the quantification and prediction of rare events characterized by extreme intensity in nonlinear waves with broad spectra. We consider a one-dimensional non- linear model with deep-water waves dispersion relation, the Majda-McLaughlin-Tabak (MMT) model, in a dynamical regime that is characterized by broadband spectrum and strong non- linear energy transfers during the development of intermittent events with finite-lifetime. To understand the energy transfers that occur...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1401.3397

0
0.0

Jun 30, 2018
06/18

by
C. Quintero-Quiroz; M. G. Cosenza

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We investigate the collective behavior of a system of chaotic Rossler oscillators indirectly coupled through a common environment that possesses its own dynamics and which in turn is modulated by the interaction with the oscillators. By varying the parameter representing the coupling strength between the oscillators and the environment, we find two collective states previously not reported in systems with environmental coupling: (i) nontrivial collective behavior, characterized by a periodic...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1404.1625

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0.0

Jun 30, 2018
06/18

by
Alexander V. Milovanov; Jens Juul Rasmussen

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The phenomena of nonlocal transport in magnetically confined plasma are theoretically analyzed. A hybrid model is proposed, which brings together the notion of inverse energy cascade, typical of drift-wave- and two-dimensional fluid turbulence, and the ideas of avalanching behavior, associable with self-organized critical (SOC) behavior. Using statistical arguments, it is shown that an amplification mechanism is needed to introduce nonlocality into dynamics. We obtain a consistent derivation of...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1403.5896

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0.0

Jun 30, 2018
06/18

by
Shijun Liao

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Yao and Hughes commented (Tellus-A, 60: 803 - 805, 2008) that "all chaotic responses are simply numerical noise and have nothing to do with the solutions of differential equations". However, using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm of the so-called "Clean Numerical Simulation" (CNS) based on the 3500th-order Taylor expansion and data in 4180-digit multiple precision, one can gain reliable, convergent chaotic solution of Lorenz...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1401.0256

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2.0

Jun 29, 2018
06/18

by
Niloofar Farajzadeh Tehrani; MohammadReza Razvan

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This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try to classify all possible dynamics. Bifurcation diagrams are obtained numerically or analytically from the mathematical model, and the parameter regions of different behaviors are clarified. The neural system exhibits a unique rest point or three ones by...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1602.08294

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1.0

Jun 29, 2018
06/18

by
Manuel Jimenez Martin; Otti D'Huys; Laura Lauerbach; Elka Korutcheva; Wolfgang Kinzel

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Chaos synchronization may arise in networks of nonlinear units with delayed couplings. We study complete and sublattice synchronization generated by resonance of two large time delays with a specific ratio. As it is known for single delay networks, the number of synchronized sublattices is determined by the Greatest Common Divisor (GCD) of the network loops lengths. We demonstrate analytically the GCD condition in networks of iterated Bernouilli maps with multiple delay times and complement our...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1602.05358

0
0.0

Jun 29, 2018
06/18

by
H. E. Gilardi-Velázquez; L. J. Ontañón-García; D. G. Hurtado-Rodriguez; E. Campos-Cantón

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A multistable system generated by a Piecewise Linear (PWL) system based on the jerky equation is presented. The systems behaviour is characterised by means of the Nearest Integer or round(x) function to control the switching events and to locate the corresponding equilibria among each of the commutation surfaces. These surfaces are generated by means of the switching function dividing the space in regions equally distributed along one axis. The trajectory of this type of system is governed by...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1611.03461

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0.0

Jun 29, 2018
06/18

by
Daniel L. Crane; Ruslan L. Davidchack; Alexander N. Gorban

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We propose a general method for constructing a minimal cover of high-dimensional chaotic attractors by embedded coherent structures, such as periodic orbits. By minimal cover we mean a finite subset of periodic orbits such that any point on the attractor is within a predefined proximity threshold to a periodic orbit within the subset. The proximity measure can be chosen with considerable freedom and adapted to the properties of a given attractor. On the example of a Kuramoto-Sivashinsky chaotic...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1607.02180

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1.0

Jun 30, 2018
06/18

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

0
0.0

Jun 30, 2018
06/18

by
Adam M Fox; Rafael de la Llave

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In this paper we identify the geometric structures that restrict transport and mixing in perturbations of integrable volume-preserving systems with nonzero net flux. Unlike KAM tori, these objects cannot be continued to the tori present in the integrable system but are generated by resonance and have a contractible direction. We introduce a remarkably simple algorithm to analyze the behavior of these maps and obtain quantitative properties of the tori. In particular, we present assertions...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1406.7569

0
0.0

Jun 30, 2018
06/18

by
Feng Liu; Zhi-Hong Guan

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In this paper, we present a unified framework of multiple attractors including multistability, multiperiodicity and multichaos. Multichaos, which means that the chaotic solution of a system lies in different disjoint invariant sets with respect to different initial values, is a very interesting and important dynamical behavior, but it is never addressed before to the best of our knowledge. By constructing a multiple logistic map, we show that multistability, multiperiodicity and multiple chaos...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1403.1657

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0.0

Jun 30, 2018
06/18

by
Greg Byrne; Christopher D. Marcotte; Roman O. Grigoriev

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Unstable nonchaotic solutions embedded in the chaotic attractor can provide significant new insight into chaotic dynamics of both low- and high-dimensional systems. In particular, in turbulent fluid flows, such unstable solutions are referred to as exact coherent structures (ECS) and play an important role in both initiating and sustaining turbulence. The nature of ECS and their role in organizing spatiotemporally chaotic dynamics, however, is reasonably well understood only for systems on...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1404.2316

0
0.0

Jun 29, 2018
06/18

by
Mirella Harsoula; Christos Efthymiopoulos; George Contopoulos

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We develop an analytical theory of chaotic spiral arms in galaxies. This is based on the Moser theory of invariant manifolds around unstable periodic orbits. We apply this theory to the chaotic spiral arms, that start from the neighborhood of the Lagrangian points L1 and L2 at the end of the bar in a barred-spiral galaxy. The series representing the invariant manifolds starting at the Lagrangian points L1, L2, or unstable periodic orbits around L1 and L2, yield spiral patterns in the...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1603.09151

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1.0

Jun 29, 2018
06/18

by
Malgorzata Bialous; Vitalii Yunko; Szymon Bauch; Michal Lawniczak; Barbara Dietz; Leszek Sirko

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We investigated experimentally the short- and long-range correlations in the fluctuations of the resonance frequencies of flat, rectangular microwave cavities that contained antennas acting as point-like perturbations. We demonstrate that their spectral properties exhibit the features typical for singular statistics. Hitherto, only the nearest-neighbor spacing distribution had been studied. We, in addition considered statistical measures for the long-range correlations and analyzed power...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1609.09233

0
0.0

Jun 29, 2018
06/18

by
Rafail V. Abramov

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The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1604.00931

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3.0

Jun 27, 2018
06/18

by
V. A. Danylenko; S. V. Mykulyak; S. I. Skurativskyi

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The article deals with the mathematical model for media with hierarchical structure. Using the hamiltonian formalism, the dynamical system describing the state of hierarchically connected structural elements was derived. According to the analysis of the Poincar\'e sections, we found the localized quasi-periodic and chaotic trajectories in the three-level hierarchical model. Moreover, studies of correlation functions shown that the power spectrum for three-level model possesses local maxima...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1503.05759

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0.0

Jun 30, 2018
06/18

by
Nazmi Burak Budanur; Predrag Cvitanović; Ruslan L. Davidchack; Evangelos Siminos

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Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation. This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the `first Fourier mode slice', a very simple, easy to implement reduction of SO(2) symmetry. While the method exhibits rapid variations in phase...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1405.1096

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0.0

Jun 30, 2018
06/18

by
Juan F. Restrepo; Gastón Schlotthauer; María E. Torres

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Approximate entropy (ApEn) has been widely used as an estimator of regularity in many scientific fields. It has proved to be a useful tool because of its ability to distinguish different system's dynamics when there is only available short-length noisy data. Incorrect parameter selection (embedding dimension $m$, threshold $r$ and data length $N$) and the presence of noise in the signal can undermine the ApEn discrimination capacity. In this work we show that $r_{max}$...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1405.7637

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0.0

Jun 30, 2018
06/18

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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0.0

Jun 28, 2018
06/18

by
Mehmet Onur Fen; Fatma Tokmak Fen

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In the present study, we investigate the existence of Li-Yorke chaos in the dynamics of shunting inhibitory cellular neural networks (SICNNs) on time scales. It is rigorously proved by taking advantage of external inputs that the outputs of SICNNs exhibit Li-Yorke chaos. The theoretical results are supported by simulations, and the controllability of chaos on the time scale is demonstrated by means of the Pyragas control technique. This is the first time in the literature that the existence as...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1512.08750

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0.0

Jun 29, 2018
06/18

by
Ingo Laut; Christoph Räth

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The performance of recurrence networks and symbolic networks to detect weak nonlinearities in time series is compared to the nonlinear prediction error. For the synthetic data of the Lorenz system, the network measures show a comparable performance. In the case of relatively short and noisy real-world data from active galactic nuclei, the nonlinear prediction error yields more robust results than the network measures. The tests are based on surrogate data sets. The correlations in the Fourier...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1610.01293

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0.0

Jun 29, 2018
06/18

by
Xiaoming Li; Shijun Liao

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In this paper we compare the reliability of numerical simulations given by the classical symplectic integrator (SI) and the clean numerical simulation (CNS) for chaotic Hamiltonian systems. The chaotic H\'{e}non-Heiles system and the famous three-body problem are used as examples for comparison. It is found that the numerical simulations given by the symplectic integrator indeed preserves the conservation of the total energy of system quite well. However, their orbits quickly depart away from...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1609.09344

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2.0

Jun 28, 2018
06/18

by
H. Bi; X. Hu; S. Boccaletti; X. Wang; Y. Zou; Z. Liu; S. Guan

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From rhythmic physiological processes to the collective behaviors of technological and natural networks, coherent phases of interacting oscillators are the foundation of the events' coordination leading a system to behave cooperatively. We unveil the existence of a new of such states, occurring in globally coupled nonidentical oscillators in the proximity of the point where the transition from the system's incoherent to coherent phase converts from explosive to continuous. In such a state,...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1511.01578

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1.0

Jun 30, 2018
06/18

by
K. Onu; F. Huhn; G. Haller

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We give an algorithmic introduction to Lagrangian coherent structures (LCSs) using a newly developed computational engine, LCS Tool. LCSs are most repelling, attracting and shearing material lines that form the centerpieces of observed tracer patterns in two-dimensional unsteady dynamical systems. LCS Tool implements the latest geodesic theory of LCSs for two-dimensional flows, uncovering key transport barriers in unsteady flow velocity data as explicit solutions of differential equations....

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1406.3527

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1.0

Jun 30, 2018
06/18

by
C. Chandre

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First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac's theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac-Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed.

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1412.4922

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1.0

Jun 30, 2018
06/18

by
John Grant; Michael Wilkinson

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We consider a spatially homogeneous advection-diffusion equation in which the diffusion tensor and drift velocity are time-independent, but otherwise general. We derive asymptotic expressions, valid at large distances from a steady point source, for the flux onto a completely permeable boundary and onto an absorbing boundary. The absorbing case is treated by making a source of antiparticles at the boundary. In both cases there is an exponential decay as the distance from the source increases;...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1412.4720

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4.0

Jun 28, 2018
06/18

by
Marius-F. Danca; Nikolay Kuznetsov; Guanrong Chen

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This paper presents some unusual dynamics of the Rabinovich-Fabrikant system, such as "virtual" saddles, "tornado"-like stable cycles and hidden chaotic attractors. Due to the strong nonlinearity and high complexity, the results are obtained numerically with some insightful descriptions and discussions.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1511.07765

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1.0

Jun 29, 2018
06/18

by
G. I. Depetri; J. C. Sartorelli; B. Marin; M. S. Baptista

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Our aim is to unveil how resonances of parametric systems are affected when symmetry is broken. We showed numerically and experimentally that odd resonances indeed come about when the pendulum is excited along a tilted direction. Applying the Melnikov subharmonic function, we not only determined analytically the loci of saddle-node bifurcations delimiting resonance regions in parameter space, but also explained these observations by demonstrating that, under the Melnikov method point of view,...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1603.00819

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2.0

Jun 29, 2018
06/18

by
E. M. Shahverdiev

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We study numerically a system of two lasers cross-coupled optoelectronically with a time delay where the output intensity of each laser modulates the pump current of the other laser. We demonstrate control of chaos via variable coupling time delay by converting the laser intensity chaos to the steady state. We also show that wavelength chaos in an electrically tunable distributed Bragg reflector laser diode with a feedback loop can be controlled via variable feedback time delay.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1605.08168

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1.0

Jun 29, 2018
06/18

by
Wojciech Szumiński; Tomasz Stachowiak

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We consider the system of two material points that interact by elastic forces according to Hooke's law and their motion is restricted to certain curves lying on the plane. The nonintegrability of this system and idea of the proof are communicated. Moreover, the analysis of global dynamics by means of Poincar\'e cross sections is given and local analysis in the neighborhood of an equilibrium is performed by applying the Birkhoff normal form. Conditions of linear stability are determined and some...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1606.03009

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2.0

Jun 29, 2018
06/18

by
M. R. Silva; E. G. Nepomuceno; G. F. V. Amaral; V. V. R. Silva

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The Chua's circuit is a paradigm for nonlinear scientific studies. It is usually simulated by means of numerical methods under IEEE 754-2008 standard. Although the error propagation problem is well known, little attention has been given to the relationship between this error and inequalities presented in Chua's circuit model. Taking the average of round mode towards $+\infty$ and $-\infty$, we showed a qualitative change on the dynamics of Chua's circuit.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.01060

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1.0

Jun 29, 2018
06/18

by
Igor A. Shepelev; Tatiana E. Vadivasova; Galina. I. Strelkova; Vadim S. Anishchenko

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We study the spatiotemporal dynamics of a ring of nonlocally coupled FitzHugh-Nagumo oscillators in the bistable regime. A new type of chimera patterns has been found in the noise-free network and when isolated elements do not oscillate. The region of existence of these structures has been explored when the coupling range and the coupling strength between the network elements are varied.

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1612.08377

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Jun 30, 2018
06/18

by
Michael Rosenblum; Arkady Pikovsky

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We analyze quasiperiodic partially synchronous states in an ensemble of Stuart-Landau oscillators with global nonlinear coupling. We reveal two types of such dynamics: in the first case the time-averaged frequencies of oscillators and of the mean field differ, while in the second case they are equal, but the motion of oscillators is additionally modulated. We describe transitions from the synchronous state to both types of quasiperiodic dynamics, and a transition between two different...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1702.08786

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5.0

Jun 30, 2018
06/18

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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5.0

Jun 30, 2018
06/18

by
Y. N. Kyrychko; K. B. Blyuss; E. Schoell

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This paper studies the stability of synchronized states in networks where couplings between nodes are characterized by some distributed time delay, and develops a generalized master stability function approach. Using a generic example of Stuart-Landau oscillators, it is shown how the stability of synchronized solutions in networks with distributed delay coupling can be determined through a semi-analytic computation of Floquet exponents. The analysis of stability of fully synchronized and of...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1406.5428

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Jun 30, 2018
06/18

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

by
A. E. Botha; W. Dednam

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The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known R\"ossler system. By optimizing the period $T$ and the three system parameters, $a$, $b$ and $c$, simultaneously, it was found that, for any initial condition $(x_0,y_0,z_0) \in \Re^3$, there exists at least one set of optimized parameters corresponding to a periodic orbit passing through $ (x_0,y_0,z_0)$. After a...

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1408.3397

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Jun 28, 2018
06/18

by
Julian Self; Michael C. Mackey

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Delay differential equations (DDE) can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to think that a random number generator (RNG) might be constructed from such a model. In this preliminary study, we consider one specific example of this and show that it satisfies criteria commonly employed in the testing of random number generators (from TestU01's very stringent "Big Crush" battery of...

Topics: Chaotic Dynamics, Nonlinear Sciences

Source: http://arxiv.org/abs/1512.07303

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Jun 27, 2018
06/18

by
Alexander P. Kuznetsov; Ludmila V. Turukina; Nikolai Yu. Chernyshov; Yuliya V. Sedova

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We consider a system of three interacting van der Pol oscillators with reactive coupling. Phase equations are derived, using proper order of expansion over the coupling parameter. The dynamics of the system is studied by means of the bifurcation analysis and with the method of Lyapunov exponent charts. Essential and physically meaningful features of the reactive coupling are discussed.

Topics: Nonlinear Sciences, Chaotic Dynamics

Source: http://arxiv.org/abs/1503.05313