Coexisting hidden and self-excited attractors in a locally active memristor-based circuit.

Abstract

This paper presents a chaotic circuit based on a nonvolatile locally active memristor model, with non-volatility and local activity verified by the power-off plot and the DC V-I plot, respectively. It is shown that the memristor-based circuit has no equilibrium with appropriate parameter values and can exhibit three hidden coexisting heterogeneous attractors including point attractors, periodic attractors, and chaotic attractors. As is well known, for a hidden attractor, its attraction basin does not intersect with any small neighborhood of any unstable equilibrium. However, it is found that some attractors of this circuit can be excited from an unstable equilibrium in the locally active region of the memristor, meaning that its basin of attraction intersects with neighborhoods of an unstable equilibrium of the locally active memristor. Furthermore, with another set of parameter values, the circuit possesses three equilibria and can generate self-excited chaotic attractors. Theoretical and simulated analyses both demonstrate that the local activity and an unstable equilibrium of the memristor are two reasons for generating hidden attractors by the circuit. This chaotic circuit is implemented in a digital signal processing circuit experiment to verify the theoretical analysis and numerical simulations.