2021/09/29 by Leila Eftekhari, Eftekhari, Leila, Mohammad M. Amirian +1 · 1 citation
Computer Science · Physics and Astronomy · #Dynamical Systems (math.DS) #FOS: Computer and information sciences #FOS: Mathematics #Neural Networks Stability and Synchronization #Neural Networks and Applications #Neural and Evolutionary Computing (cs.NE) #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2109.14383
openalex publication_date 2021/09/29 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
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.