Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network

Lafranceschina, Jacopo; Wackerbauer, Renate

doi:10.1063/1.4907193

Cited by 11 publications

(5 citation statements)

References 43 publications

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“…Such a configuration has, to our knowledge, not yet been demonstrated, and it extends the usual notion of a chaotic saddle in spatially extended systems, in the sense that it provides a mechanism for switchings between more than two distinct space-time patterns. Transient spatiotemporal chaos studied in other systems governed by a chaotic saddle usually exhibits one type of dynamics [87,88] or at most two alternative patterns as observed in a neuronal network [86] or in a modified complex Ginzburg-Landau equation on two spatial subdomains [41].…”

Section: Discussionmentioning

confidence: 99%

“…Most of these examples, however, have in common that the chaotic saddle is characterized by one type of spatiotemporal dynamics. Recently it has been reported that in transient spatiotemporal chaos the alternation between two different space-time patterns either on the whole spatial domain [86] or on two subdomains [41] can be observed. By contrast, the chaotic saddle identified here has a more complicated structure since it contains three different space-time patterns and an irregular switching between them mediated by channel-like structures in phase space.…”

Section: Manifolds and Phase Spacementioning

confidence: 99%

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Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

2016

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We report on self-induced switchings between multiple distinct space-time patterns in the dynamics of a spatially extended excitable system. These switchings between low-amplitude oscillations, nonlinear waves, and extreme events strongly resemble a random process, although the system is deterministic. We show that a chaotic saddle-which contains all the patterns as well as channel-like structures that mediate the transitions between them-is the backbone of such a pattern switching dynamics. Our analyses indicate that essential ingredients for the observed phenomena are that the system behaves like an inhomogeneous oscillatory medium that is capable of self-generating spatially localized excitations and that is dominated by short-range connections but also features long-range connections. With our findings, we present an alternative to the well-known ways to obtain self-induced pattern switching, namely noise-induced attractor hopping, heteroclinic orbits, and adaptation to an external signal. This alternative way can be expected to improve our understanding of pattern switchings in spatially extended natural dynamical systems like the brain and the heart.

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Section: Discussionmentioning

confidence: 99%

Section: Manifolds and Phase Spacementioning

confidence: 99%

Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

2016

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“…There are many studies of spatiotemporal patterns in systems of excitable cells (Fujii and Tsuda 2004 ; Hartle and Wackerbauer 2017 ; Keplinger and Wackerbauer 2014 ; Lafranceschina and Wackerbauer 2014 ; Mondal et al. 2018 ; Calim et al.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

et al. 2022

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Spatiotemporal patterns are common in biological systems. For electrically coupled cells, previous studies of pattern formation have mainly used applied current as the primary bifurcation parameter. The purpose of this paper is to show that applied current is not needed to generate spatiotemporal patterns for smooth muscle cells. The patterns can be generated solely by external mechanical stimulation (transmural pressure). To do this we study a reaction-diffusion system involving the Morris–Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling — in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and that the spatially extended model exhibits spatiotemporal chaos. We also use travelling wave coordinates to analyse travelling waves.

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“…Many studies have been published on spatiotemporal patterns in networks of excitable cells [28,35,49,54,65,12]. Tsyganov et.…”

Section: Introductionmentioning

confidence: 99%

Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Fatoyinbo¹,

Brown²,

Simpson³

et al. 2021

Preprint

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Spatiotemporal patterns are common in biological systems. For electrically-coupled cells previous studies of pattern formation have mainly used external forcing as the main bifurcation parameter. The purpose of this paper is to show that spatiotemporal patterns in electrically-coupled smooth muscle cells occur even in the absence of forcing. We study a reaction-diffusion system with the Morris-Lecar equations and observe a wide range of spatiotemporal patterns for different values of the model parameters. Some aspects of these patterns are explained via a bifurcation analysis of the system without coupling -in particular Type I and Type II excitability both occur. We show the patterns are not due to a Turing instability and use travelling wave coordinates to analyse travelling waves.

show abstract

Impact of weak excitatory synapses on chaotic transients in a diffusively coupled Morris-Lecar neuronal network

Cited by 11 publications

References 43 publications

Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

Self-Induced Switchings between Multiple Space-Time Patterns on Complex Networks of Excitable Units

Pattern Formation in a Spatially Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

Pattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells

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