4.5 Article

Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure

期刊

COGNITIVE NEURODYNAMICS
卷 17, 期 4, 页码 1045-1059

出版社

SPRINGER
DOI: 10.1007/s11571-022-09844-9

关键词

Fractional calculus; Bifurcation; Stability; Memristor; Hopfield neural network

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This paper presents a method of constructing neural networks using fractional-order memristors, revealing the relationship between network stability and fractional-order value, number of neurons, and network structure through analysis of stability conditions and numerical simulations.
A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of n sub-network neurons, increasing the synchronization in the network. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the n-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.

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