Showing papers on "Coupled map lattice published in 2017"

Characterization of spatiotemporal chaos in a Kerr optical frequency comb and in all fiber cavities

Abstract: Complex spatiotemporal dynamics have been a subject of recent experimental investigations in optical frequency comb microresonators and in driven fiber cavities with Kerr-type media. We show that this complex behavior has a spatiotemporal chaotic nature. We determine numerically the Lyapunov spectra, allowing us 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 identify a wide regime of parameters where the system exhibits a coexistence between the spatiotemporal chaos, the oscillatory localized structure, and the homogeneous steady state. The destabilization of an oscillatory localized state through radiation of counter-propagating fronts between the homogeneous and the spatiotemporal chaotic states is analyzed. To characterize better the spatiotemporal chaos, we estimate the front speed as a function of the pump intensity.

A Chaotic System with Two Stable Equilibrium Points: Dynamics, Circuit Realization and Communication Application

Abstract: Recent evidence suggests that a system with only stable equilibria can generate chaotic behavior. In this work, we study a chaotic system with two stable equilibrium points. The dynamics of the system is investigated via phase portrait, bifurcation diagram and Lyapunov exponents. The feasibility of the system is introducing its electronic realization. Moreover, the chaotic system is used in Symmetric Chaos Shift Keying (SCSK) and Chaotic ON-OFF Keying (COOK) modulated communication designs for secure communication. It is determined that the SCSK modulated communication system implemented with the chaotic system is more successful than COOK modulation for secure communication.

A new chaotic map with three isolated chaotic regions

Abstract: Intriguing as the discovery of new chaotic maps is, some new maps also bring new nonlinear phenomena of iterative map behavior. In this paper, we present a simple two-dimensional chaotic map which has three totally separated regions. The twin regions, creating strange and interesting attractors, are close to each other and vertically reflected however not identical in shape, while the distant region, generating a Henon-like attractor, starts with period-doubling until complete chaos. Given the unusual behavior of the map introduced in this paper, we initially presented linear stability and bifurcation analysis per regions, with Lyapunov exponents and largest exponent computation. Besides the standardized calculations, what we focus here is to find out how a simple map can exhibit different chaotic behaviors in different regions.

Weakly coupled map lattice models for multicellular patterning and collective normalization of abnormal single-cell states.

Abstract: We present a weakly coupled map lattice model for patterning that explores the effects exerted by weakening the local dynamic rules on model biological and artificial networks composed of two-state building blocks (cells). To this end, we use two cellular automata models based on (i) a smooth majority rule (model I) and (ii) a set of rules similar to those of Conway's Game of Life (model II). The normal and abnormal cell states evolve according to local rules that are modulated by a parameter κ. This parameter quantifies the effective weakening of the prescribed rules due to the limited coupling of each cell to its neighborhood and can be experimentally controlled by appropriate external agents. The emergent spatiotemporal maps of single-cell states should be of significance for positional information processes as well as for intercellular communication in tumorigenesis, where the collective normalization of abnormal single-cell states by a predominantly normal neighborhood may be crucial.

Spatiotemporal and synchronous chaos in accumulated coupled map lattice

Abstract: The onset of spatiotemporal chaos in coupled map lattice (CML) with a new coupling scheme called accumulated CML is studied in this paper. A rigorous proof of the existence of chaos in the sense of Li–Yorke is presented. Also the range of the coupling strength in which global synchronization can be obtained is calculated by stability analysis of the synchronized state. Finally, the positivity of Lyapunov exponents confirms the existence of chaos.

Relating high dimensional stochastic complex systems to low-dimensional intermittency

Abstract: We evaluate the implication and outlook of an unanticipated simplification in the macroscopic behavior of two high-dimensional sto-chastic models: the Replicator Model with Mutations and the Tangled Nature Model (TaNa) of evolutionary ecology. This simplification consists of the apparent display of low-dimensional dynamics in the non-stationary intermittent time evolution of the model on a coarse-grained scale. Evolution on this time scale spans generations of individuals, rather than single reproduction, death or mutation events. While a local one-dimensional map close to a tangent bifurcation can be derived from a mean-field version of the TaNa model, a nonlinear dynamical model consisting of successive tangent bifurcations generates time evolution patterns resembling those of the full TaNa model. To advance the interpretation of this finding, here we consider parallel results on a game-theoretic version of the TaNa model that in discrete time yields a coupled map lattice. This in turn is represented, a la Langevin, by a one-dimensional nonlinear map. Among various kinds of behaviours we obtain intermittent evolution associated with tangent bifurcations. We discuss our results.

Chaotic systems based on jerk equation and discrete maps with scaling parameters

Abstract: In the recent decades, applications of chaotic systems have flourished in various fields Hence, there is an increasing demand on generalized, modified and novel chaotic systems In this paper, we combine the general equation of jerk-based chaotic systems with simple scaled discrete chaotic maps Numerical simulations of the properties of two systems, each with four control parameters, are presented The parameters show interesting behaviors and dependencies among them In addition, they exhibit controlling capabilities of the ranges of system responses, hence the size of the attractor diagram Moreover, these behaviors and dependencies are analogous to those of the corresponding discrete chaotic maps

On the Network Analysis of the State Space of Discrete Dynamical Systems

Abstract: This paper discusses the letter entitled “Network analysis of the state space of discrete dynamical systems” by A. Shreim et al. [Phys. Rev. Lett. 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 1D cellular automata.

The dynamical properties of even shift space

Abstract: A dynamical system is a system that evolves with time. Research in the field of dynamical system is largely focused on the nature of chaos on that system. Nowadays, there are various definitions of chaotic dynamical systems. However, the most well-known definition of chaos is Devaney chaos that states three chaotic conditions in its definition; sensitivity dependence on initial conditions, transitivity and density of periodic points. In this paper, we are investigating the presence of chaotic behavior in a discrete space, even shift. The even shift space is a space of all infinite sequences over symbols 0 and 1 such that between any two 1’s there are an even number of 0’s. By the end of this investigation, we prove that even shift space is not only Devaney chaos but also satisfies some other stronger chaotic conditions i.e. totally transitive, topologically mixing, blending, and locally everywhere onto.A dynamical system is a system that evolves with time. Research in the field of dynamical system is largely focused on the nature of chaos on that system. Nowadays, there are various definitions of chaotic dynamical systems. However, the most well-known definition of chaos is Devaney chaos that states three chaotic conditions in its definition; sensitivity dependence on initial conditions, transitivity and density of periodic points. In this paper, we are investigating the presence of chaotic behavior in a discrete space, even shift. The even shift space is a space of all infinite sequences over symbols 0 and 1 such that between any two 1’s there are an even number of 0’s. By the end of this investigation, we prove that even shift space is not only Devaney chaos but also satisfies some other stronger chaotic conditions i.e. totally transitive, topologically mixing, blending, and locally everywhere onto.

Simulation Of Chaotic Dynamics For Chaos Based Optimization - An Extended Study.

Abstract: This paper discuss the utilization of the complex chaotic dynamics given by the selected time-continuous chaotic systems as well as by the discrete chaotic maps, as the chaotic pseudo random number generators and driving maps for the chaos based optimization. Such an optimization concept is utilizing direct output iterations of chaotic system transferred into the required numerical range or it uses the chaotic dynamics for mapping the search space mostly within the local search techniques. This paper shows totally three groups of complex chaotic dynamics given by chaotic flows, oscillators and discrete maps. Simulations of examples of chaotic dynamics mapped to the search space were performed and related issues like parametric plots, distributions of such a systems, periodicity, and dependency on internal accessible parameters are briefly discussed in this paper.

Escaping from a chaotic saddle in the presence of noise

Abstract: There are certain situations in noisy nonlinear dynamical systems, for which it is required a fast transition between a chaotic and a periodic state. Here, we present a novel procedure to achieve this goal in the context of the partial control method of chaotic systems. The partial control method is a recently developed control procedure, that allows to keep the dynamics of a system showing transient chaos, close to its chaotic saddle. In this kind of systems, and in absence of an external control, trajectories remain chaotic for a while in a certain region of phase space before eventually escaping towards an external attractor. The aim of the control algorithm proposed here, is to maintain the chaotic orbits as much time as we want close to the chaotic saddle before forcing an immediate escape. To do that, we use the safe sets defined in the partial control method in a completely different way. By only using this set, we show how possible is to handle the stabilisation and destabilisation of the chaotic dynamics of the partially controlled system.

Some Chaotic Properties of a Coupled Lattice System Related with Belusov-Zhabotinsky Reaction

Abstract: In Guirao (MATCH Commun Math Comput Chem 64:335–344, 2010) studied distributional chaos of a family of coupled lattice dynamical systems (CLSs) which generalize the model stated by Kaneko (Phys Rev Lett 65:1391–1394, 1990). He also presented a definition of distributional chaos on a sequence (DCS) for CLSs and stated two different sufficient conditions for a given CLS to exhibit DCS. Inspired by his work, in this paper we explore some chaotic properties of the map which is deduced by a kind of coupled map lattice (CML). In particular, some sufficient conditions under which a given CML is \((\mathcal {F}_{1},\mathcal {F}_{2})\)-chaotic, \(\omega \)-chaotic or topologically chaotic are obtained. And the conclusions discussed above are examined when the metric changes. Moreover, it is pointed out that some CMLs can be simplified to a simpler CLS.

On static control of swarm systems

Abstract: In this article, there is reported our progress of our research that merges evolutionary (swarm) algorithms, (complex) networks, and coupled map lattices. The article is mainly focused on the statical control of the self-organizing migrating algorithm. There is described how to convert networks into a coupled map lattices, how to create a feedback loop into the algorithm, and how to control the run of the algorithm through the coupled map lattice. Also, you can find here a small revision of our previous research. All experiments are done on a well known CEC 2015 benchmarks.

An investigation of phenomena observed in scale-free coupled circle map

Abstract: In this study, phenomena observed in scale-free coupled circle map are investigated. The circle map is a one-dimensional discrete-time dynamical system which exhibits various kinds of behavior as the parameters change. As the high-dimensional coupled circle map, the coupled map lattice and the globally coupled map have been studied. However, the scale-free coupled circle map has not been well investigated so far. We study the model in which one of the circle maps corresponding to a hub node of the scale-free network has the parameter which leads the single circle map to generate high-order periodic points, and the parameter values of the other maps are set to converge to a fixed point. Changing the coupling strength between each map, we investigated the synchronization in the scale-free coupled circle map by calculating the value of the order parameter. The result of this study elucidated that when the coupling strength between each map was negative, all circle maps in the network behaved chaotic whatever the parameter value of the hub node was set to. That means the phenomena was generated because of the scale-free network structure itself but not the state of the hub node. On the other hand, the coupling strength was positive, the behavior observed in the network was based on the state of the hub node. In addition, the result showed the periodic point observed in the hub node could change to the fixed point after the scale-free network generated. The result suggests that the phenomena such as chaos and periodic oscillation could change to be converged into stable fixed point by forming the scale-free network and appropriately controlling the parameters.

Dynamics analysis and numerical simulations of a new 5D Lorenz-type chaos dynamical system

Abstract: Ultimate bound sets of chaotic systems have important applications in chaos control and chaos synchronization. Ultimate bound sets can also be applied in estimating the dimensions of chaotic attractors. However, it is often a difficult work to obtain the bounds of high-order chaotic systems due to complex algebraic structure of high-order chaotic systems. In this paper, a new 5D autonomous quadratic chaotic system which is different from the Lorenz chaotic system is proposed and analyzed. Ultimate bound sets and globally exponential attractive sets of this system are studied by introducing the Lyapunov-like functions. To validate the ultimate bound estimation, numerical simulations are also investigated. c ©2017 All rights reserved.