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Chaos Collection


 
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Chaos : Cryptanalysis of a chaotic communication scheme using adap...

By: Ying Liu and Wallace K. S. Tang

Description: This paper addresses the cryptanalysis of a secure communication scheme recently proposed by Wu [Chaos 16, 043118 (2006) ], where the information signal is modulated into a system parameter of a unified chaotic system. With the Kerckhoff principle, assuming that the structure of the cryptosystem is known, an adaptive observer can be designed to synchronize the targeted system, so that the transmitted information and the user-specific parameters are obtained....

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Chaos : Pinning synchronization of delayed neural networks

By: Jin Zhou, Xiaoqun Wu, Wenwu Yu, Michael Small, and Jun-an Lu

Description: This paper investigates adaptive pinning synchronization of a general weighted neural network with coupling delay. Unlike recent works on pinning synchronization which proposed the possibility that synchronization can be reached by controlling only a small fraction of neurons, this paper aims to answer the following question: Which neurons should be controlled to synchronize a neural network? By using Schur complement and Lyapunov function methods, it is pro...

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Chaos : Synchronization of a class of chaotic systems with fully u...

By: M. Roopaei and M. Zolghadri Jahromi

Description: In this paper, an adaptive sliding mode control method for synchronization of a class of chaotic systems with fully unknown parameters is introduced. In this method, no knowledge of the bounds of parameters is required in advance and the parameters are updated through an adaptive control process. We use our proposed method to synchronize two chaotic gyros, which has been the subject of intense study during the recent years for its application in the navigati...

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Chaos : Stability and multiple bifurcations of a damped harmonic o...

By: Yongli Song, Tonghua Zhang, and Moses O. Tadé

Description: We investigate the dynamics of a damped harmonic oscillator with delayed feedback near zero eigenvalue singularity. We perform a linearized stability analysis and multiple bifurcations of the zero solution of the system near zero eigenvalue singularity. Taking the time delay as the bifurcation parameter, the presence of steady-state bifurcation, Bogdanov–Takens bifurcation, triple zero, and Hopf-zero singularities is demonstrated. In the case when the system...

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Chaos : On the bifurcation of species

By: M.A.Bees,P.H.Coullet, and E.A.Spiegel

Description: We propose and analyze a model of evolution of species based upon a general description of phenotypes in terms of a single quantifiable characteristic. In the model, species spontaneously arise as solitary waves whose members almost never mate with those in other species, according to the rules laid down. The solitary waves in the model bifurcate and we interpret such events as speciation. Our aim in this work is to determine whether a generic mathematical m...

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Chaos : Complete periodic synchronization in coupled systems

By: Wei Zou and Meng Zhan

Description: Recently, complete chaotic synchronization in coupled systems has been well studied. In this paper, we study complete synchronization in coupled periodic oscillators with diffusive and gradient couplings. Eight typical types of critical curve for the transverse Lyapunov exponent of standard mode, which give rise to different synchronization-desynchronization patterns, are classified. All possible desynchronous behaviors including steady state, periodic state...

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Chaos : Coherence resonance induced by colored noise near Hopf bif...

By: Juan Ma, Tiejun Xiao, Zhonghuai Hou, and Houwen Xin

Description: Effects of colored noise near supercritical Hopf bifurcation, especially noise induced oscillation (NIO) and coherence resonance (CR), have been studied analytically in the Brusselator model, using the stochastic normal form method. Two types of colored noise are considered: one is the standard Gaussian colored noise generated by the Ornstein–Uhlenbeck (OU) process and the other is the so-called power-limited (PL) process. Depending on the noise intensity an...

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Chaos : An equivalent condition for a sequence to be the sequence ...

By: Fryderyk Falniowski

Description: We show that a sequence is the sequence of partial entropies of some dynamical system with respect to a partition of the phase space if and only if it is non-negative, increasing, and has decreasing increments.

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Chaos : Filtering by nonlinear systems

By: E. Campos Cantón, J. S. González Salas, and J. Urías

Description: Synchronization of nonlinear systems forced by external signals is formalized as the response of a nonlinear filter. Sufficient conditions for a nonlinear system to behave as a filter are given. Some examples of generalized chaos synchronization are shown to actually be special cases of nonlinear filtering.

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Chaos : Perception-action map learning in controlled multiscroll s...

By: Paolo Arena, Sebastiano De Fiore, Luigi Fortuna, and Luca Patané

Description: In this paper a new technique for action-oriented perception in robots is presented. The paper starts from exploiting the successful implementation of the basic idea that perceptual states can be embedded into chaotic attractors whose dynamical evolution can be associated with sensorial stimuli. In this way, it can be possible to encode, into the chaotic dynamics, environment-dependent patterns. These have to be suitably linked to an action, executed by the ...

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Chaos : Improvements and applications of entrainment control for n...

By: Fang Liu, Qiang Song, and Jinde Cao

Description: This paper improves the existing entrainment control approaches and develops unified schemes to chaos control and generalized (lag, anticipated, and complete) synchronization of nonlinear dynamical systems. By introducing impulsive effects to the open-loop control method, we completely remove its restrictions on goal dynamics and initial conditions, and derive a sufficient condition to estimate the upper bound of impulsive intervals to ensure the global asym...

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Chaos : Modulational instability in a purely nonlinear coupled com...

By: Fabien II Ndzana, Alidou Mohamadou, and Timoléon C. Kofané

Description: We study wave propagation in a nonlinear transmission line with dissipative elements. We show analytically that the telegraphers' equations of the electrical transmission line can be modeled by a pair of continuous coupled complex Ginzburg–Landau equations, coupled by purely nonlinear terms. Based on this system, we investigated both analytically and numerically the modulational instability (MI). We produce characteristics of the MI in the form of typical de...

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Chaos : Spatiotemporal system reconstruction using Fourier spectra...

By: Daolin Xu and Omid Khanmohamadi

Description: A technique based on trigonometric spectral methods and structure selection is proposed for the reconstruction, from observed time series, of spatiotemporal systems governed by nonlinear partial differential equations of polynomial type with terms of arbitrary derivative order and nonlinearity degree. The system identification using Fourier spectral differentiation operators in conjunction with a structure selection procedure leads to a parsimonious model of...

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Chaos : Beyond harmonic sounds in a simple model for birdsong prod...

By: Ana Amador and Gabriel B. Mindlin

Description: In this work we present an analysis of the dynamics displayed by a simple bidimensional model of labial oscillations during birdsong production. We show that the same model capable of generating tonal sounds can present, for a wide range of parameters, solutions which are spectrally rich. The role of physiologically sensible parameters is discussed in each oscillatory regime, allowing us to interpret previously reported data.

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Chaos : The development of truncated inviscid turbulence and the F...

By: G. Ooms and B. J. Boersma

Description: A study was made of the possible similarity between the development of truncated, inviscid turbulence and the Fermi–Pasta–Ulam (FPU) problem. For the case of a constant time scale, which resembles the FPU problem, a significant increase in the time to achieve equipartition was found when the initial energy was decreased. At first a few modes were generated and only rather late in the spectral development other modes appear and equipartition was established.

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Chaos : Phase synchronization in tilted inertial ratchets as chaot...

By: José L. Mateos and Fernando R. Alatriste

Description: The phenomenon of phase synchronization for a particle in a periodic ratchet potential is studied. We consider the deterministic dynamics in the underdamped case where the inertia plays an important role since the dynamics can become chaotic. The ratchet potential is tilted due to a constant external force and is rocking by an external periodic forcing. This potential has to be tilted in order to obtain a rotator or self-sustained nonlinear oscillator in the...

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Chaos : Global dissipativity analysis on uncertain neural networks...

By: Qiankun Song and Jinde Cao

Description: In this paper, the problems of global dissipativity and global exponential dissipativity are investigated for uncertain neural networks with discrete time-varying delay and distributed time-varying delay as well as general activation functions. By constructing appropriate Lyapunov–Krasovskii functionals and employing Newton–Leibniz formulation and linear matrix inequality (LMI) technique, several new criteria for checking the global dissipativity and global ...

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Chaos : Vortex filament dynamics in computational models of ventri...

By: Richard H. Clayton

Description: In three-dimensional cardiac tissue, the re-entrant waves that sustain ventricular fibrillation rotate around a line of phase singularity or vortex filament. The aim of this study was to investigate how the behavior of these vortex filaments is influenced by membrane kinetics, initial conditions, and tissue geometry in computational models of excitable tissue. A monodomain model of cardiac tissue was used, with kinetics described by a three-variable simplifi...

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Chaos : Stability diagram for the forced Kuramoto model

By: Lauren M. Childs and Steven H. Strogatz

Description: We analyze the periodically forced Kuramoto model. This system consists of an infinite population of phase oscillators with random intrinsic frequencies, global sinusoidal coupling, and external sinusoidal forcing. It represents an idealization of many phenomena in physics, chemistry, and biology in which mutual synchronization competes with forced synchronization. In other words, the oscillators in the population try to synchronize with one another while al...

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Chaos : Synchronization of chaotic systems with uncertain chaotic ...

By: Zheng-Ming Ge and Cheng-Hsiung Yang

Description: We study the synchronization of general chaotic systems which satisfy the Lipschitz condition only, with uncertain chaotic parameters by linear coupling and pragmatical adaptive tracking. The uncertain parameters of a system vary with time due to aging, environment, and disturbances. A sufficient condition is given for the asymptotical stability of common zero solution of error dynamics and parameter update dynamics by the Ge–Yu–Chen pragmatical asymptotical...

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