LAUSR

Due to the introduction of ideal memristors, extreme multistability has been found in many autonomous memristive circuits. However, such extreme multistability has not yet been reported in a non-autonomous memristive circuit. To this end, this paper presents an improved non-autonomous memristive FitzHugh–Nagumo circuit that possesses a smooth hyperbolic tangent memductance nonlinearity, from which coexisting infinitely many attractors are obtained. By utilizing voltage–current circuit model, a three-dimensional non-autonomous dynamical model is established, based on which the initial-dependent dynamics is explored by numerical plots and extreme multistability is thereby exhibited. To confirm that the improved non-autonomous memristive circuit operates in hidden oscillating patterns, an accurate two-dimensional non-autonomous dimensionality reduction model with initial-related parameters is further built by using incremental integral transformation, upon which stability analysis and bifurcation behaviors are elaborated. Because the equilibrium state of the dimensionality reduction model is always a stable node-focus, hidden extreme multistability with coexisting infinitely many attractors is truly confirmed. Finally, PSIM circuit simulations validate the initial-related hidden dynamical behaviors.