A fractional-order discrete memristor neuron model: Nodal and network dynamics

Janarthanan Ramadoss; Asma Alharbi; Karthikeyan Rajagopal; Salah Boulaaras; Janarthanan Ramadoss; Asma Alharbi; Karthikeyan Rajagopal; Salah Boulaaras

doi:10.3934/era.2022202

Electronic Research Archive

2022, Volume 30, Issue 11: 3977-3992. doi: 10.3934/era.2022202

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Research article

A fractional-order discrete memristor neuron model: Nodal and network dynamics

1.
Center for Artificial Intelligence, Chennai Institute of Technology, Chennai 600069, India
2.
Department of Mathematics, College of Sciences and Arts, ArRass, Qassim University 52571, Saudi Arabia
3.
Center for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
4.
Department of Electronics and Communications Engineering, University Centre for Research & Development, Chandigarh University, Mohali 140413, Punjab, India

Received: 12 April 2022 Revised: 16 June 2022 Accepted: 23 June 2022 Published: 05 September 2022

We discuss the dynamics of a fractional order discrete neuron model with electromagnetic flux coupling. The discussed neuron model is a simple one-dimensional map which is modified by considering flux coupling. We consider a discrete fractional order memristor to mimic the effects of electromagnetic flux on the neuron model. The bifurcation dynamics of the fractional order neuron map show an inverse period-doubling route to chaos as a function of control parameters, namely the fractional order of the map and the flux coupling coefficient. The bifurcation dynamics of the systems are derived both in the time and frequency domains. We present a two-parameter phase diagram using the Lyapunov exponent to categorize the various dynamics present in the system. In addition to the Lyapunov exponent, we use the entropy of the model to distinguish the various dynamics of the systems. To investigate the network behavior of the fractional order neuron map, a lattice array of $ N\times N $ nodes is constructed and external periodic stimuli are applied to the network. The formation of spiral waves in the network and the impact of various parameters, like the fractional order, flux coupling coefficient and the coupling strength on the wave propagation are also considered in our analysis.
- fractional order discrete neuron model,
- memristor,
- Lyapunov exponents,
- entropy,
- spiral waves
Citation: Janarthanan Ramadoss, Asma Alharbi, Karthikeyan Rajagopal, Salah Boulaaras. A fractional-order discrete memristor neuron model: Nodal and network dynamics[J]. Electronic Research Archive, 2022, 30(11): 3977-3992. doi: 10.3934/era.2022202

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Abstract

We discuss the dynamics of a fractional order discrete neuron model with electromagnetic flux coupling. The discussed neuron model is a simple one-dimensional map which is modified by considering flux coupling. We consider a discrete fractional order memristor to mimic the effects of electromagnetic flux on the neuron model. The bifurcation dynamics of the fractional order neuron map show an inverse period-doubling route to chaos as a function of control parameters, namely the fractional order of the map and the flux coupling coefficient. The bifurcation dynamics of the systems are derived both in the time and frequency domains. We present a two-parameter phase diagram using the Lyapunov exponent to categorize the various dynamics present in the system. In addition to the Lyapunov exponent, we use the entropy of the model to distinguish the various dynamics of the systems. To investigate the network behavior of the fractional order neuron map, a lattice array of $ N\times N $ nodes is constructed and external periodic stimuli are applied to the network. The formation of spiral waves in the network and the impact of various parameters, like the fractional order, flux coupling coefficient and the coupling strength on the wave propagation are also considered in our analysis.

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