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Synchronization and Pattern Formation in a Memristive Diffusive Neuron Model

Sanjeev Kumar Sharma

Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India

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Arnab Mondal

Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India

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Argha Mondal

School of Engineering, Amrita Vishwa Vidyapeetham, Amritapuri, Kollam 690525, India

Department of Mathematical Sciences, University of Essex, Wivenhoe Park, UK

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Ranjit Kumar Upadhyay

https://orcid.org/0000-0002-1210-7804

Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad 826004, India

E-mail Address: ranjit.chaos@gmail.com

Corresponding author.

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, and

Jun Ma

Department of Physics, Lanzhou University of Technology, Lanzhou 730050, P. R. China

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https://doi.org/10.1142/S0218127421300305Cited by:11 (Source: Crossref)

Abstract

In this article, we construct an excitable memristive diffusive neuron model by considering a biophysical slow–fast bursting oscillator and study the effects of electromagnetic induction on the dynamics of the single model as well as the coupled systems. We explore various firing regimes such as tonic spiking, bursting, and mixed-mode oscillations depending on the bifurcation structure with different injected current stimuli, then perform a comparative analysis on the synchronization of the coupled oscillators by setting the model into two different network architectures. First, a diffusively coupled network is considered, and later a global network is constructed. The results suggest that the diffusively connected neurons show complete synchronization at higher couplings for bursting and tonic spiking regimes. Furthermore, we show that the extended spatial system can generate spiral-like patterns in the vicinity of a Hopf bifurcation point and observe the impact of Gaussian white noise to study its effects on pattern formation. These types of patterns are robust in the excitable model. Our results might contribute significantly to the dynamical studies of irregular neural computation.

Keywords:

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