Multi-scroll dynamics and coexisting attractors in electromagnetic-induced Hopfield networks

Abstract

Excitatory and inhibitory neuronal activity generates neural oscillations, these oscillations are vital for functioning of brain. Improving knowledge about these neural oscillations helps us better comprehend neurological disorders. This article explores a 4D Hopfield neural network combined with memristive electromagnetic induction and pulse current stimulation, which has practical significance in the emerging field of artificial intelligence. The research analyzes the dynamical behavior of proposed Hopfield network consisting of four neurons by supplying external stimulus to second neuron via memristor and exposing fourth neuron to pulse current. Lyapunov exponents and bifurcation diagrams are studied with the choice of memristive internal parameter as bifurcation parameter. As a result of sensitivity to initial conditions, various biscroll and multilayer attractors are generated illustrating their state transitions with time series plots. In addition, coexisting bifurcation and attractors are presented for different selection of multilevel-logic pulse current and it is observed that the pulse current parameter governs the number of scrolls and structure of attractors. Multilayer attractors corresponding to the external input applied to the memristor elements are displayed to investigate the transition of the system states through time series plots and phase plane portraits. This work, in particular, improves our understanding of brain activity while also providing insights into the neural mechanisms, leading to neurological conditions.