Long-range patterns in Hindmarsh–Rose networks

Etémé, Armand Sylvin; Tabi, Conrad Bertrand; Mohamadou, Alidou

doi:10.1016/j.cnsns.2016.07.005

Cited by 38 publications

(11 citation statements)

References 42 publications

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“…Along the same line, the observed time series highlight the effect of the intensity of the stimulus on the shape of the membrane potential which is characterized by spiking regime for ν=0.53, bursting regime for ν=1.0 and chaotic regime when ν=1.5. These results are in perfect agreement with those obtained in the [9][10][11][12] where neurons are commonly excited by the external current I ext . In this case, it has been established that [18] spiking, bursting and chaotic modes are obtained when, 1.32<I ext <1.57, 1.57<I ext <2.92 and 2.92<I ext <3.4, respectively.…”

Section: Neurons Firing Induced By Dna Dynamicssupporting

confidence: 90%

Neuronal firing and DNA dynamics in a neural network

Etémé

Tabi²,

Ateba

et al. 2018

J. Phys. Commun.

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We study the mutual effects of neuronal electrical activity and DNA dynamics in a network of electrically coupled neurons with nearest neighbors communication. For that we develop by means of the coupling function method, a mathematical DNA-neuron model that can be considered as an extension of the simplified Hodgkin-Huxley models. Numerically, we explore the biological properties of the model with emphasis on local phase transitions and synchronous neural activity. Our results suggest that firing and coherent behavior of neural network are controlled by DNA dynamics. Conversely, neuronal activity induces DNA electrochemical denaturation. As a result, we expect that the prominent DNA-neuron model would be worth in controlling gene expression and neurodegenerative diseases in the sensory thalamus.

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Section: Neurons Firing Induced By Dna Dynamicssupporting

confidence: 90%

Neuronal firing and DNA dynamics in a neural network

Etémé

Tabi²,

Ateba

et al. 2018

J. Phys. Commun.

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“…Based on their localization properties, breather solitons have been used as models of rogue waves (RWs) whose behaviors and characteristics are not yet fully unmasked, mainly because they may appear suddenly, propagate within short times, destroy everything on their way and disappear without any trace [1,2]. For instance, it has been well established that they may appear in physical systems as the consequence of the interplay between nonlinear and dispersive effects, under the activation of the so-called MI phenomenon [3][4][5][6][7][8]. Recently, interest in studying RWs has gone beyond oceanography and hydrodynamics [9,10] to reach some other areas related to optics and photonics [11][12][13][14], Bose-Einstein condensation [15][16][17], biophysics [18][19][20][21], plasma physics [22,23], just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

2019

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Relativistic ion-acoustic waves are investigated in an electronegative plasma. The use of the reductive perturbation method summarizes the hydrodynamic model to a nonlinear Schrödinger equation which supports the occurrence of modulational instability (MI). From the MI criterion, we derive a critical value for the relativistic parameter 1 , below which MI may develop in the system. The MI analysis is then conducted considering the presence and absence of negative ions, coupled to effects of relativistic parameter and the electron-to-negative ion temperature ratio. Under high values of the latter, additional regions of instability are detected, and their spatial expansion is very sensitive to the change in 1 and may support the appearance of rogue waves whose behaviors are discussed. The parametric analysis of super-rogue wave amplitude is performed, where its enhancement is debated relatively to changes in 1 , in the presence and absence of negative ions.

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“…The other parameters, except for external synaptic current I, have the following fixed values: a = 1, b = 3, c = 1, d = 5, s = 4 and x 0 = −8/5. The coupling strength between the neurons is chosen to be D 0 = 0.1, which corresponds to a relatively strong connection between the pair of neurons, but within a biologically reasonable range [19][20][21]23]. The parameter I plays the role of the bifurcation parameter in our work.…”

Section: The Main System Of Equationmentioning

confidence: 99%

“…In this work we study a minimally possible network of two interacting Hindmarsh -Rose neurons. Here we consider the three-dimensional Hindmarsh -Rose systems describing each neuron, and the coupling force caused by the electric link between the neurons [21][22][23]. We also suppose that the neurons are identical, which is quite a strong condition.…”

Section: Introductionmentioning

confidence: 99%

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

Garashchuk¹

2021

Nelin. Dinam.

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We study a minimal network of two coupled neurons described by the Hindmarsh – Rose model with a linear coupling. We suppose that individual neurons are identical and study whether the dynamical regimes of a single neuron would be stable synchronous regimes in the model of two coupled neurons. We find that among synchronous regimes only regular periodic spiking and quiescence are stable in a certain range of parameters, while no bursting synchronous regimes are stable. Moreover, we show that there are no stable synchronous chaotic regimes in the parameter range considered. On the other hand, we find a wide range of parameters in which a stable asynchronous chaotic regime exists. Furthermore, we identify narrow regions of bistability, when synchronous and asynchronous regimes coexist. However, the asynchronous attractor is monostable in a wide range of parameters. We demonstrate that the onset of the asynchronous chaotic attractor occurs according to the Afraimovich – Shilnikov scenario. We have observed various asynchronous firing patterns: irregular quasi-periodic and chaotic spiking, both regular and chaotic bursting regimes, in which the number of spikes per burst varied greatly depending on the control parameter.

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Long-range patterns in Hindmarsh–Rose networks

Cited by 38 publications

References 42 publications

Neuronal firing and DNA dynamics in a neural network

Neuronal firing and DNA dynamics in a neural network

Low relativistic effects on the modulational instability of rogue waves in electronegative plasmas

Asynchronous Chaos and Bifurcations in a Model of Two Coupled Identical Hindmarsh – Rose Neurons

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