Modulational instability in chain diffusive neuronal networks under electric field

Takembo, Clovis Ntahkie; Fouda, H. P. Ekobena; Kofané, Timoléon Crépin

doi:10.1007/s12648-022-02368-2

Cited by 4 publications

(1 citation statement)

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“…The authors showed that by using phase-locked loop systems as nodes of the networks, dynamical regimes such as quasiharmonic oscillations, spiking, bursting, and chaotic behavior are based on different network typologies such as star, ring, chain, and random architectures. The dynamical and physiological effects of the presence of electric field on an improved version of FitzHugh-Nagumo model was investigated in [45]. Using the multiple scale expansion method on the system of N-differential equations, the authors obtained the angular frequency of the modulated impulse wave along the network.…”

Section: Introductionmentioning

confidence: 99%

Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Muni

Njitacke

Feudjio

et al. 2022

Chaos Theory and Applications

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In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.

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Section: Introductionmentioning

confidence: 99%