Coexisting Infinitely Many Nonchaotic Attractors in a Memristive Weight-Based Tabu Learning Neuron

Abstract

Memristive synaptic weight is a changeable connection synaptic weight. It reflects the self-adaption physical processing in biological neurons. To study its dynamical effect, this paper presents a memristive synaptic weight-based tabu learning neuron model. It is constructed by replacing the resistive self-connection synaptic weight in the tabu learning neuron with a memristive self-connection synaptic weight. The equilibrium point of the memristive tabu learning model is time-varying and switches between no equilibrium state and line equilibrium state with the change of the external current. Particularly, the stability of the line equilibrium state closely relies on the initial state of the memristor, resulting in the emergence of coexisting infinitely many nonchaotic attractors. By employing the bifurcation plots, Lyapunov exponents, and phase plots, this paper numerically reveals the initial state-switched coexisting bifurcation behaviors and initial state-relied extreme multistability, and thereby discloses the coexisting infinitely many nonchaotic attractors composed of mono-periodic, multiperiodic, and quasi-periodic orbits. In addition, PSIM circuit simulations and printed-circuit board-based experiments are executed and the coexisting infinitely many nonchaotic attractors are realized physically. The results well verify the numerical simulations.