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

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 withi...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-10, Vol.12 (19), p.2970
Main Authors: Almatroud, Othman Abdullah, Pham, Viet-Thanh, Rajagopal, Karthikeyan
Format: Article
Language:English
Subjects:
Behavior
bifurcation
Bifurcations
Design and construction
Electric current rectifiers
Equipment and supplies
Impact analysis
Liapunov exponents
Lyapunov exponent
Magnetic flux
Memristors
Morris–Lecar neuron model
multistability
Neural networks
Neurons
Neurosciences
Parameter modification
Potassium
Rectifier instruments
ReLU-based memristor
Synchronism
synchronization
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Description
Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12192970