Transient and steady coexisting attractors in a new memristor-based 4-D chaotic circuit

Abstract

In this study, a new current-controlled memristor is proposed and its characteristics are analyzed. Based on this new memristor, a new four-dimensional chaotic circuit is proposed. The complex dynamics of the proposed chaotic circuit are investigated. From the results of the theoretical analysis and the numerical simulations, it is found that the memristor-based chaotic circuit can generate different types of attractors including single-scroll, double-scroll, and periodic attractors for varying circuit parameters. By taking symmetrical initial conditions, symmetric steady coexisting attractors are obtained under the same set of circuit parameters. For certain initial conditions, striking transient coexisting attractors with different timescales can be obtained. In particular, there are two transient changes occurring successively at different time scales respect to the same initial conditions for the proposed chaotic circuit, which is a novel dynamic property. Finally, a practical circuit platform that describes the proposed chaotic circuit on Field Programmable Gate Arrays (FPGA) is designed, and some experimental results are presented for confirmation.