Hidden extreme multistability and its control with selection of a desired attractor in a non-autonomous Hopfield neuron

Abstract

In this article, a single nonautonomous Hopfield neuron is investigated. This neuron involves a new hyperbolic-type memristor as self-synaptic weight. The current–voltage characteristics of the new memristor enables the observation of the hysteresis loop with more than one pinch. The analysis of the equilibria highlighted that the model has hidden dynamics. A plethora of nonlinear phenomena is obtained during the analysis of the model. Among them, the coexistence of an infinite number of symmetric bifurcation diagrams each having its intrinsic energetic singularity. The zooms of the initial condition diagrams enable to observe the coexistence of ten periodic hidden attractors and nine chaotic hidden attractors. The model also exhibited the antimonotonicity phenomenon characterized by the coexistence of an infinite number of bubbles. The control of up to nine coexisting hidden chaotic attractors in a specific domain of the initial condition is successfully realized. This control is achieved by choosing initially an attractor as a designated survivor using the feedback term method. It is then found that the employed method can also be used to control multistability in a system without an equilibrium point. An analog circuit of the model is also designed in PSpice, to further support the results of the theoretical investigations.