Stability Analysis of Fractional Order Memristor Synapse-coupled Hopfield Neural Network with Ring Structure
This work addresses stability analysis for neural networks with memory properties, which is incremental as it extends existing models by incorporating fractional calculus and ring structures.
The paper tackled the stability of a fractional-order memristor synapse-coupled Hopfield neural network with a ring structure, finding that stability depends on the fractional-order value and number of neurons, with numerical simulations showing potential routes to chaos as the fractional order increases.
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.