Enhancing synchrony in multiplex network due to rewiring frequency

Rakshit, Sarbendu; Bera, Bidesh K.; Kurths, Jürgen; Ghosh, Dibakar

doi:10.1098/rspa.2019.0460

Cited by 14 publications

(3 citation statements)

References 30 publications

(33 reference statements)

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“…For instance, in a network of Hindmarsh-Rose neurons in which the coupling structure of both electrical and chemical synapses is time-varying, it has been found that the coupling strength required for the achievement of complete synchrony is significantly lower for increasing the rewiring frequency 50 . Moreover, the enhancement effect has been also observed in a network with multiple layers in which only the structure of specific layers is time-varying 51 . Furthermore, it has been shown that diverse partial synchronization patterns can be generated by multi-plexing of adaptive networks 52 .…”

mentioning

confidence: 90%

Interlayer synchronization in time-varying Kuramoto-Sakaguchi networks

Eser¹,

Rıza²

2021

Preprint

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confidence: 90%

Interlayer synchronization in time-varying Kuramoto-Sakaguchi networks

Eser¹,

Rıza²

2021

Preprint

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“…Multiplex network is a subclass of multilayer networks, where one-to-one interactions between all the nodes in different layers are maintained [15], [16]. In recent time, collective dynamics in multi-layered networks has been extensively explored [15], [1], [17], [18], [19], [20], [21], [22] including investigations on chimera states [23], [24] and explosive synchronization [25], [26]. In such multilayer dynamical networks [27], [28], [29], synchrony is one of the most important desired states for all practical purposes since it is essential for the efficient performance of the networks.…”

Section: Introductionmentioning

confidence: 99%

Resilience in multiplex networks by addition of cross-repulsive links

Saha

2022

Preprint

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A multiplex network of identical dynamical units becomes resilient against parameter perturbation by adding selective linear diffusive cross-coupling links. A parameter drift at any instant in one or multiple network nodes can destroy synchrony, causing failure and even collapse in the network performance. We introduced [Phys. Rev. E95, 062204(2017)] a recovery strategy by selective addition of cross-coupling links to save synchrony in the network from the edge of failure due to parameter mismatch (small or large) in any nodes. This concept is extended to 2-layered multiplex networks when the emergent synchrony becomes resilient against a small or large parameter drifting. In addition, the stability of the synchronous state is enhanced from local stability to global stability of synchrony. By the addition of cross-coupling, the network revives complete synchrony in all the nodes except the perturbed nodes, which emerges into a type of generalized synchrony with all the unperturbed nodes. The generalized synchrony is manifested simply by a linear amplitude response in the state variable(s) of the perturbed node(s) by a scaling factor proportional to the mismatch. A set of systematic rules has been derived from the linear flow matrix of the dynamical system representing the nodes' dynamics that helps find the connectivity matrix of the cross-coupling links. Lyapunov function stability condition is used to determine the cross-coupling link strength that, in turn, establishes global stability of synchrony of the multiplex network. We verify the efficacy of our proposed coupling scheme with analytical results and numerical simulations of two examples of multiplex networks. In the first example, we use nonlocal connectivity in each layer with nodal dynamics of the FitzHugh-Nagumo neuron model. Furthermore, we use a second example of a two-layered multiplex network of chaotic R össler systems with random connectivity in both layers. We confirm that our results are generic, independent of nodes' dynamics and network topology.

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“…These synchronized states can emerge as the effect of the static or time-varying interactions in either attractive or repulsive couplings [19]. Moreover, enormous effort has been devoted to the controllability and observability of synchronized complex networks [20], improving the synchronizability [21,22] and robustness of synchronization [23].…”

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confidence: 99%

Converting high-dimensional complex networks to lower-dimensional ones preserving synchronization features

Naseri

Parastesh

Ghassemi

et al. 2022

EPL

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Studying the stability of synchronization of coupled oscillators is one of the prominent topics in network science. However, in most cases, the computational cost of complex network analysis is challenging because they consist of a large number of nodes. This study includes overcoming this obstacle by presenting a method for reducing the dimension of a large-scale network, while keeping the complete region of stable synchronization unchanged. To this aim, the first and last non-zero eigenvalues of the Laplacian matrix of a large network are preserved using the eigen-decomposition method and, Gram-Schmidt orthogonalization. The method is only applicable to undirected networks and the result is a weighted undirected network with smaller size. The reduction method is studied in a large-scale a small-world network of Sprott-B oscillators. The results show that the trend of the synchronization error is well maintained after node reduction for different coupling schemes.

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Enhancing synchrony in multiplex network due to rewiring frequency

Cited by 14 publications

References 30 publications

Interlayer synchronization in time-varying Kuramoto-Sakaguchi networks

Interlayer synchronization in time-varying Kuramoto-Sakaguchi networks

Resilience in multiplex networks by addition of cross-repulsive links

Converting high-dimensional complex networks to lower-dimensional ones preserving synchronization features

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