Noise-Induced Macroscopic Bifurcations in Globally Coupled Chaotic Units

Monte, Silvia De; d’Ovidio, Francesco; Chaté, Hugues; Mosekilde, Erik

doi:10.1103/physrevlett.92.254101

Cited by 20 publications

(23 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Such non-trivial collective behavior (NTCB) is now known to be quite generic, being observed whether interactions are local or global, time variable is discrete or continuous [5][6][7][8], and evolution is deterministic or noisy [9][10][11]. One of the most interesting features of NTCB is that microscopic chaos can coexist with macroscopic evolutions of different instability -periodic, quasi-periodic, and even chaotic in the case of global coupling [4,12].…”

Section: Introductionmentioning

confidence: 99%

Collective Lyapunov modes

Takeuchi¹,

Chaté²

2013

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

Abstract. We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors, they act collectively on the trajectory and hence characterize the instability of its collective dynamics. We further develop, for globally-coupled systems, a connection between these collective modes and the Lyapunov modes in the corresponding PerronFrobenius equation. We thereby address the fundamental question of the effective dimension of collective dynamics and discuss the extensivity of chaos in presence of collective dynamics.

show abstract

Section: Introductionmentioning

confidence: 99%

Collective Lyapunov modes

Takeuchi¹,

Chaté²

2013

J. Phys. A: Math. Theor.

Self Cite

View full text Add to dashboard Cite

show abstract

“…To study the collective behavior directly, the return map is employed [12,13], and the relationship between the SMLE and return map is compared. The arithmetic average of the state value of every lattice in the subsystem is expressed as…”

Section: Return Map For Collective Behavior Of Subsystem Versus Smlementioning

confidence: 99%

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

Shi

2011

Chin. Sci. Bull.

View full text Add to dashboard Cite

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.

show abstract

“…Section 6 summarizes the main results of the paper, discusses the perspectives of our method and points to a number of possible applications. Part of our results have been presented in [9].…”

Section: Introductionmentioning

confidence: 99%

“…We present an analytical method for deriving the collective behavior from the single element dynamics and the statistical features of the microscopic disorder [9]. Expanding in series the equation of motion of the "mean-field" (i.e.…”

Section: Introductionmentioning

confidence: 99%

Effects of microscopic disorder on the collective dynamics of globally coupled maps

Monte

d’Ovidio

Chaté

et al. 2005

Physica D: Nonlinear Phenomena

Self Cite

View full text Add to dashboard Cite

This paper studies the effect of independent additive noise on the synchronous dynamics of large populations of globally coupled maps. Our analysis is complementary to the approach taken by Teramae and Kuramoto [39] who pointed out the anomalous scaling properties preceding the loss of coherence. We focus on the macroscopic dynamics that remains deterministic at any noise level and differs from the microscopic one. Using properly defined order parameters, an analytical approach is proposed for describing the collective dynamics in terms of an approximate lowdimensional system. The systematic derivation of the macroscopic equations provides a link between the microscopic features of the population (single-element dynamics and noise distribution) and the properties of the emergent behaviour. The macroscopic bifurcations induced by noise are compared to those originating from parameter mismatches within the population.

show abstract

Noise-Induced Macroscopic Bifurcations in Globally Coupled Chaotic Units

Cited by 20 publications

References 40 publications

Collective Lyapunov modes

Collective Lyapunov modes

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

Effects of microscopic disorder on the collective dynamics of globally coupled maps

Contact Info

Product

Resources

About