The effects of synaptic time delay on motifs of chemically coupled Rulkov model neurons

Franović, Igor; Miljković, Vladimir D.

doi:10.1016/j.cnsns.2010.05.007

Cited by 18 publications

(7 citation statements)

References 53 publications

(83 reference statements)

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“…The effect of delay in in-phase and anti-phase synchronization was the object of Franovic and Miljkovic (2011) in Rulkov map neural network connected by reciprocal sigmoid chemical synapses.…”

Section: Impulsive Couplingmentioning

confidence: 99%

A brief history of excitable map-based neurons and neural networks

Girardi‐Schappo

Tragtenberg

Kinouchi

2013

Journal of Neuroscience Methods

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This review gives a short historical account of the excitable maps approach for modeling neurons and neuronal networks. Some early models, due to Pasemann (1993), Chialvo (1995) and Kinouchi and Tragtenberg (1996), are compared with more recent proposals by Rulkov (2002) and Izhikevich (2003).We also review map-based schemes for electrical and chemical synapses and some recent findings as critical avalanches in map-based neural networks.We conclude with suggestions for further work in this area like more efficient maps, compartmental modeling and close dynamical comparison with conductance-based models.

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Section: Impulsive Couplingmentioning

confidence: 99%

A brief history of excitable map-based neurons and neural networks

Girardi‐Schappo

Tragtenberg

Kinouchi

2013

Journal of Neuroscience Methods

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“…Many applications of single-neuron models already exist, but it seems that a systematic study of their response as a function of the control parameters lack. Map-based models are easier to treat and analyze and have been used to describe specific situations, especially when considering coupled elements characterized by chemical [28,29], electrical [30,31] or both aspects [32][33][34][35]. The topology of neural networks is also an essential player in their dynamical behavior, as reported for, e.g., scalefree [32], global [36], mean-field [37], small world [38], and Apollonian [39,40] networks.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper is to explore the control parameter space of one of the most popular and successful discrete model for neurons, namely a map proposed by Rulkov [21]. This model reproduces well many neural behaviors such as emergent bursting from nonbursting cells [19], spiking-bursting [21] and the origin of chaos [46], the birth of self-sustained subthreshold oscillations [47], patterns of bursting [48], spatiotemporal chaos ordering [49], or synchronization features in two neurons [28,50], in large one-dimensional neural networks [42] and two-dimensional lattices [22], and also in scale-free [35,43,51] and in small-world networks [52,53]. The great interest in Rulkov's model lies in the fact that it can reproduce quite well the spiking and spiking-bursting behaviors observed in real-life neurons [20,21].…”

Section: Introductionmentioning

confidence: 99%

Distribution of spiking and bursting in Rulkov’s neuron model

Ramírez-Ávila

Depickère

Jánosi

et al. 2022

Eur. Phys. J. Spec. Top.

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Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

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“…[18][19][20] The Rulkov model is actively used in the study of complex dynamics of neural networks. [21][22][23][24][25] Multistability is one of the reasons that significantly complicate the behavior of dynamical systems. 26 It is well known that in nonlinear systems, even weak inevitable random disturbances can cause new diverse dynamical regimes, which are not observed in initial unforced models.…”

Section: Introductionmentioning

confidence: 99%

Stochastic transformations of multi-rhythmic dynamics and order–chaos transitions in a discrete 2D model

Tsvetkov

Bashkirtseva

Ryashko

2021

Chaos: An Interdisciplinary Journal of Nonlinear Science

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A problem of the analysis of stochastic effects in multirhythmic nonlinear systems is investigated on the basis of the conceptual neuron map-based model proposed by Rulkov. A parameter zone with diverse scenarios of the coexistence of oscillatory regimes, both spiking and bursting, was revealed and studied. Noise-induced transitions between basins of periodic attractors are analyzed parametrically by statistics extracted from numerical simulations and by a theoretical approach using the stochastic sensitivity technique. Chaos-order transformations of dynamics caused by random forcing are discussed.

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The effects of synaptic time delay on motifs of chemically coupled Rulkov model neurons

Cited by 18 publications

References 53 publications

A brief history of excitable map-based neurons and neural networks

A brief history of excitable map-based neurons and neural networks

Distribution of spiking and bursting in Rulkov’s neuron model

Stochastic transformations of multi-rhythmic dynamics and order–chaos transitions in a discrete 2D model

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