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

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 property, we should use mathematical frameworks like fractional calculus, which capable of doing so. Here, first present fractional-order synapse-coupling Hopfield network on two neurons then extend model with ring structure consists n sub-network neurons, increasing synchronization in network. Necessary sufficient conditions for stability equilibrium points are investigated, highlighting dependency value number neurons. Numerical simulations bifurcation analysis, along Lyapunov exponents, given two-neuron case substantiates theoretical findings, suggesting possible routes towards chaos when order system increases. In n-neuron also, it revealed depends sub-networks.