Coupled dynamics on networks

Amritkar, R. E.; Jalan, Sarika

doi:10.1016/j.physa.2004.08.044

Cited by 10 publications

(4 citation statements)

References 14 publications

(21 reference statements)

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“…In N inter , coupling between two isolated nodes is not included. The criteria for the distinction of different cluster states are as follows [34]: The state, corresponding to f intra = 0 and f inter > 0, is defined as the ideal D cluster state as the mechanism behind the synchronization is intercluster couplings, and the state corresponding to f intra > 0 and f inter ∼ N cl k /N c (N cl is the number of clusters) is defined as the ideal SO cluster state as the mechanism behind the synchronization between pairs of nodes is due to intercluster couplings. Further, if |f intra − f inter < th, the clusters are of mixed type.…”

Section: Synchronized and Phase Synchronized Clustersmentioning

confidence: 99%

Impact of heterogeneous delays on cluster synchronization

Jalan

Singh

2014

Phys. Rev. E

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We investigate cluster synchronization in coupled map networks in the presence of heterogeneous delays. We find that while the parity of heterogeneous delays plays a crucial role in determining the mechanism of cluster formation, the cluster synchronizability of the network gets affected by the amount of heterogeneity. In addition, heterogeneity in delays induces a rich cluster pattern as compared to homogeneous delays. The complete bipartite network stands as an extreme example of this richness, where robust ideal driven clusters observed for the undelayed and homogeneously delayed cases dismantle, yielding versatile cluster patterns as heterogeneity in the delay is introduced. We provide arguments behind this behavior using a Lyapunov function analysis. Furthermore, the interplay between the number of connections in the network and the amount of heterogeneity plays an important role in deciding the cluster formation.

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Section: Synchronized and Phase Synchronized Clustersmentioning

confidence: 99%

Impact of heterogeneous delays on cluster synchronization

Jalan

Singh

2014

Phys. Rev. E

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“…We take the value of µ = 4, for which individual un-coupled unit shows chaotic behavior with the value of Lyapunov exponent being ln 2. As an effect of coupling the coupled dynamics 1 shows various different kinds of coherent behavior, such as synchronization [16], phase-synchronization [14,19,22,33] and other large scale macroscopic coherence [35] depending upon the coupling architecture and the coupling strength. In this paper we consider synchronization x i (t) = x j (t) for all i, j and all initial conditions, and phasesynchronization as considered in [34,19].…”

Section: Coupled Dynamics On Networkmentioning

confidence: 99%

Transition from the self-organized to the driven dynamical clusters

Singh

Jalan

2012

Physica A: Statistical Mechanics and its Applications

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We study the mechanism of formation of synchronized clusters in coupled maps on networks with various connection architectures. The nodes in a cluster are self- synchronized or driven-synchronized, based on the coupling strength and underlying network structures. A smaller coupling strength region shows driven clusters independent of the network rewiring strategies, whereas a larger coupling strength region shows the transition from the self-organized cluster to the driven cluster as network connections are rewired to the bi-partite type. Lyapunov function analysis is performed to understand the dynamical origin of cluster formation. The results provide insights into the relationship between the topological clusters which are based on the direct connections between the nodes, and the dynamical clusters which are based on the functional behavior of these nodes.Comment: 18 pages, 7 figure

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“…Some current directions of research include exploring the synchronization of component states [21], [22], robustness of dynamical expression [23], [24] and the coupled dynamics of states and network structures [25].…”

Section: Dynamics Occurring On Networkmentioning

confidence: 99%

The Self-Organization of Interaction Networks for Nature-Inspired Optimization

Whitacre

Sarker

Pham

2008

IEEE Trans. Evol. Computat.

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Abstract-Over the last decade, significant progress has been made in understanding complex biological systems, however there have been few attempts at incorporating this knowledge into nature inspired optimization algorithms. In this paper, we present a first attempt at incorporating some of the basic structural properties of complex biological systems which are believed to be necessary preconditions for system qualities such as robustness. In particular, we focus on two important conditions missing in Evolutionary Algorithm populations; a selforganized definition of locality and interaction epistasis. We demonstrate that these two features, when combined, provide algorithm behaviors not observed in the canonical Evolutionary Algorithm or in Evolutionary Algorithms with structured populations such as the Cellular Genetic Algorithm. The most noticeable change in algorithm behavior is an unprecedented capacity for sustainable coexistence of genetically distinct individuals within a single population.This capacity for sustained genetic diversity is not imposed on the population but instead emerges as a natural consequence of the dynamics of the system.

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Coupled dynamics on networks

Cited by 10 publications

References 14 publications

Impact of heterogeneous delays on cluster synchronization

Impact of heterogeneous delays on cluster synchronization

Transition from the self-organized to the driven dynamical clusters

The Self-Organization of Interaction Networks for Nature-Inspired Optimization

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