Complex dynamics in chain HNN with parameter-relied equilibria and memristive electromagnetic induction

Investigating the dynamics of neural networks under electromagnetic induction contributes to understanding the complex electrical activity in the brain. This paper proposes a memristive chain Hopfield neural network (MCHNN) containing unidirectional synaptic connections, where a flux-controlled memristor mimics the electromagnetic induction between neurons. Under different parameters, the equilibria of MCHNN have different numbers and properties, thus producing diverse dynamics. Numerical analysis shows that there are diverse coexisting attractors, such as point attractors and periodic and chaotic attractors, which are yielded from different initial conditions. Moreover, the memristor's internal parameter can be considered as a special signal controller. It acts on the oscillation amplitude of the neuron's output signal, along with amplitude control and offset-boosting about the flux. By building a feasible hardware platform, the numerical analysis outcomes are supported, and the existence of the proposed MCHNN is verified. In addition, the NIST test outcomes indicate that MCHNN has good pseudo-randomness and is suitable for engineering applications.