Analytical results for coupled-map lattices with long-range interactions

Anteneodo, Celia; Pinto, Sandro Ely de Souza; Batista, Antônio M.; Viana, Ricardo L.

doi:10.1103/physreve.68.045202

Cited by 54 publications

(18 citation statements)

References 41 publications

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“…Another related case of interest is to consider different types of local dynamics and different types of ranges for coupling [19][20][21][22][23][24][25][26][27][28] in investigating the variations in patterns of collective behaviors as well as the SMLE. Considering the non-extensivity of the long-range coupling case, nonextensive statistical mechanics may be applied for a deeper understanding of numerical results [29].…”

Section: Discussionmentioning

confidence: 99%

Collective behavior of coupled map lattices with different scales of local coupling

Shi

2011

Chin. Sci. Bull.

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In this paper, I present a numerical study on the collective behavior of one-dimensional coupled map lattices with the nearest coupling to different scales for the whole system. Using the maximum Lyapunov exponent as a tool for subsystem and return mapping, I observed several basic patterns of collective behavior and investigated the contrasts between the different scales. To study the mechanism, the system under entirely random perturbations was investigated using the Monte Carlo method and the contrast with the deterministic approach is given. The results show that the response to a random input is complicated and involves the correlation of different signals and taking into consideration the dynamic properties of the system itself. subsystem, maximum Lyapunov exponent, different scale, return map, random perturbation Citation:Shi W J. Collective behavior of coupled map lattices with different scales of local coupling.Space-time chaos has been studied for many years and is still a major topic of research. Using coupled map lattices (CMLs) as a basic model for studying space-time chaos has received increased attention for some time [1]. Previous research on this model has mainly been applied to global dynamics, while little consideration of the dynamics has been given to different scales of the system as the lattices were assumed to be coarse grained. However, if the system has some collective behavior, the dynamics for different scales of the system should be considered. On the other hand, the relationship between few and many bodied systems continues to attract great interest. A similar pertinent question is whether I can also treat the dynamics of the CML with a deterministic approach and add random perturbations? An interesting paper [2] gives a positive answer to this for a special case, although random noise is artificially added. From the research presented in this paper, it is clear that the question is a difficult one. Furthermore, recent works related to nontrivial collective behavior has attracted wide attention. In particular, using Lyapunov modes gives a very new and profound comprehension of collective spatiotemporal chaotic behaviors [3]. In this paper, I aim to carry out a numerical study of collective behaviors for various local scales of the whole system (the scale here is the length of a subsystem). Common and extensively studied models (CML) are employed.

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Section: Discussionmentioning

confidence: 99%

Collective behavior of coupled map lattices with different scales of local coupling

Shi

2011

Chin. Sci. Bull.

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“…KS-entropy or metric entropy measures how chaotic a dynamical system is and proportional to the rate at which information about the state of system is lost in the course of time or iteration [18]. Using the invariant measure, the [KS-entropy] of symmetric N-dimensional map can be written as [16,19]:…”

Section: Kolmogorov-sinai Entropy In Synchronized Statementioning

confidence: 99%

Global Synchronization & Anti-Synchronization in N-Coupled Map Lattices

et al. 2007

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By considering a symmetric N-dimensional map which possesses invariant measure in its diagonal and anti-diagonal invariant sub-manifolds, we have been able to propose an N-coupled map which possesses invariant measure in synchronized or anti-synchronized states. Then chaotic synchronization and anti-synchronization are investigated in the introduced model. We have calculated Kolmogrov-Sinai entropy and Lyapunov exponent as another tool to study the stability of N-coupled map in synchronized and anti-synchronization states.

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“…At the outset, note that, while coupled smooth dynamical systems are widespread in the literature, very few results are available for coupled non-smooth systems, with the research in this direction being focused mostly on coupled piecewise linear onedimensional maps [21,22,32], such as tent maps [24,25] or generalizations of piecewise linear Markov maps [23]. So, although non-smooth systems are widespread in engineering [33,34], economics [35], ecology [36,37] and biology [38,39], the exploration of such systems under coupling in wide ranging topologies has been limited.…”

Section: Introductionmentioning

confidence: 99%

Effect of switching links in networks of piecewise linear maps

Sinha

2015

Nonlinear Dyn

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We investigate the spatiotemporal behaviour of a network where the local dynamics at the nodes (sites) is governed by piecewise linear maps. The local maps we consider exhibit the interesting and potentially useful property of robust chaos. We study the coupled system of such maps with varying fraction of random non-local connections, where the random links may be static, or may change over time. While this system is always unsynchronized under regular connections, synchronized chaos emerges when some of the links are rewired randomly. Further, increasing the frequency of link changes and fraction of random links significantly enhances the range of synchronization. Additionally, dynamic random links are also found to suppress unbounded dynamics in parameter regimes where blow-ups occurred under regular coupling.

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Analytical results for coupled-map lattices with long-range interactions

Cited by 54 publications

References 41 publications

Collective behavior of coupled map lattices with different scales of local coupling

Collective behavior of coupled map lattices with different scales of local coupling

Global Synchronization & Anti-Synchronization in N-Coupled Map Lattices

Effect of switching links in networks of piecewise linear maps

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