Effect of switching links in networks of piecewise linear maps

De, Suparna; Sinha, Sudeshna

doi:10.1007/s11071-015-2103-4

Cited by 7 publications

(2 citation statements)

References 43 publications

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“…( 2) in the paper [60]) during simulations of FitzHugh-Nagumo neuronal models. Heterogeneity in time is introduced by considering the network having time-varying links [61][62][63] depending on the two coupling probabilities P µ and P σ , which govern the update of the coupling topology with each iteration n. The probability with which the central node is connected to all the peripheral nodes at a particular n is denoted by P µ . Likewise, the probability with which the peripheral nodes are connected to their R neighboring nodes is given by P σ .…”

Section: System Modellingmentioning

confidence: 99%

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Ghosh

Muni

Fatoyinbo

2023

Preprint

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We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology not only varying in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that update the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have a wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters.

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Section: System Modellingmentioning

confidence: 99%

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Ghosh

Muni

Fatoyinbo

2023

Preprint

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“…Most studies have assumed the interactions among the nodes to be invariant over time. However in recent times there have been efforts to incorporate a time-varying links, namely changing connections between the units in a dynamical network [3][4][5][6][7][8][9][10][11][12]. Such time varying interactions model the evolution of connections over time, and are commonly found in physical, biological, social and engineered systems [13][14][15][16][17].…”

Section: Introductionmentioning

confidence: 99%

Suppression and revival of oscillations through time-varying interaction

Chaurasia

Choudhary

Shrimali

et al. 2019

Chaos, Solitons & Fractals

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We explore the dynamical consequences of switching the coupling form in a system of coupled oscillators. We consider two types of switching, one where the coupling function changes periodically and one where it changes probabilistically. We find, through bifurcation diagrams and Basin Stability analysis, that there exists a window in coupling strength where the oscillations get suppressed. Beyond this window, the oscillations are revived again. A similar trend emerges with respect to the relative predominance of the coupling forms, with the largest window of fixed point dynamics arising where there is balance in the probability of occurrence of the coupling forms. Further, significantly, more rapid switching of coupling forms yields large regions of oscillation suppression. Lastly, we propose an effective model for the dynamics arising from switched coupling forms and demonstrate how this model captures the basic features observed in numerical simulations and also offers an accurate estimate of the fixed point region through linear stability analysis.

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Role of network topology in noise reduction using coupled dynamics

Kohar

Kia

et al. 2016

Nonlinear Dyn

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Effect of switching links in networks of piecewise linear maps

Cited by 7 publications

References 43 publications

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

On the analysis of a heterogeneous coupled network of memristive Chialvo neurons.

Suppression and revival of oscillations through time-varying interaction

Role of network topology in noise reduction using coupled dynamics

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