Chaos, synchronization, and emergent behaviors in memristive hopfield networks: bi-neuron and regular topology analysis

Abstract

This paper investigates the dynamics of a Hopfield inertial bi-neuron with double memristive synaptic weights. The dynamical behavior of the system is investigated with both numerical and analytical studies to characterize the proposed model, which has up to thirty-nine equilibrium points. In this model, numerical simulations show many behaviors such as chaos, antimonotonicity of periodic and chaotic bubbles, and bursting oscillation (regular and irregular). Moreover, this system showed multiple coexistence of up to six different attractors, with the attractor basins confirming this phenomenon. A ring and star network of Hopfield neurons was also considered. We found interesting spatio-temporal regimes, including chimera and cluster states. Moreover, we showed a striking coexistence of synchronized, chimera, and cluster states in the network. The integration of multiple memristors in neural network systems holds promise for improving our understanding of the brain and developing more sophisticated artificial intelligence technologies that can better mimic human cognitive abilities.