A FRACTIONAL DIFFERENCE EQUATION MODEL OF A SIMPLE NEURON MAP

Salem Alkhalaf, Suresh Kumarasamy (), Sundaram Arun (), Anitha Karthikeyan () and Salah Boulaaras ()
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Salem Alkhalaf: Department of Computer Science, College of Science and Arts at ArRass, Qassim University, Buraydah, Saudi Arabia
Suresh Kumarasamy: Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
Sundaram Arun: Electronics and Communication Engineering, Jerusulaem College of Engineering, Chennai, Tamilnadu, India
Anitha Karthikeyan: Department of Electronics and Communications Engineering and University, Centre of Research & Development, Chandigarh University, Mohali 140413, Punjab, India
Salah Boulaaras: Department of Mathematics, College of Sciences, Qassim University, Saudi Arabia

FRACTALS (fractals), 2022, vol. 30, issue 10, 1-7

Abstract: In this work, we present the dynamics of the one dimension fractional-order Rulkov map of biological neurons. The one-dimensional neuron map shows all the dynamical behaviors observed in the real-time experiment. The integer order one-dimensional Rulkov map exhibits chaotic dynamics in the presence of time-dependent external stimuli like periodic sinusoidal force or random Gaussian process. When we construct a large complex network of neurons, the higher system dimension, as well as the external forcing, is always an obstacle. Interestingly, our study shows even with constant external stimuli, the fractional-order one-dimensional neuron shows a rich variety of complex dynamics including chaotic dynamics. We present our results based on the Lyapunov exponent of the fractional-order systems.

Keywords: One-Dimensional Neuronal Model; Fractional-Order Neuronal Model; Caputo Fractional Difference Equation (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1142/S0218348X22402630

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