Complex dynamics in a Hopfield neural network under electromagnetic induction and electromagnetic radiation

Due to the potential difference between two neurons and that between the inner and outer membranes of an individual neuron, the neural network is always exposed to complex electromagnetic environments. In this paper, we utilize a hyperbolic-type memristor and a quadratic nonlinear memristor to emulate the effects of electromagnetic induction and electromagnetic radiation on a simple Hopfield neural network (HNN), respectively. The investigations show that the system possesses an origin equilibrium point, which is always unstable. Numerical results uncover that the HNN can present complex dynamic behaviors, evolving from regular motions to chaotic motions and finally to regular motions, as the memristors' coupling strength changes. In particular, coexisting bifurcations will appear with respect to synaptic weights, which means bi-stable patterns. In addition, some physical results obtained from breadboard experiments confirm Matlab analyses and Multisim simulations.