A Rectified Linear Unit-Based Memristor-Enhanced Morris–Lecar Neuron Model

Othman Abdullah Almatroud, Viet-Thanh Pham () and Karthikeyan Rajagopal
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Othman Abdullah Almatroud: Department of Mathematics, Faculty of Science, University of Ha’il, Ha’il 2440, Saudi Arabia
Viet-Thanh Pham: Faculty of Electronics Technology, Industrial University of Ho Chi Minh City, Ho Chi Minh City 70000, Vietnam
Karthikeyan Rajagopal: Center for Research, Easwari Engineering College, Chennai 600089, India

Mathematics, 2024, vol. 12, issue 19, 1-10

Abstract: This paper introduces a modified Morris–Lecar neuron model that incorporates a memristor with a ReLU-based activation function. The impact of the memristor on the dynamics of the ML neuron model is analyzed using bifurcation diagrams and Lyapunov exponents. The findings reveal chaotic behavior within specific parameter ranges, while increased magnetic strength tends to maintain periodic dynamics. The emergence of various firing patterns, including periodic and chaotic spiking as well as square-wave and triangle-wave bursting is also evident. The modified model also demonstrates multistability across certain parameter ranges. Additionally, the dynamics of a network of these modified models are explored. This study shows that synchronization depends on the strength of the magnetic flux, with synchronization occurring at lower coupling strengths as the magnetic flux increases. The network patterns also reveal the formation of different chimera states, such as traveling and non-stationary chimera states.

Keywords: Morris–Lecar neuron model; ReLU-based memristor; bifurcation; Lyapunov exponent; multistability; synchronization; chimera state (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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