Riddled Attraction Basin and Multistability in Three-Element-Based Memristive Circuit

Author:

Xu Quan1ORCID,Tan Xiao1,Zhang Yunzhen2,Bao Han3ORCID,Hu Yihua4,Bao Bocheng1ORCID,Chen Mo1ORCID

Affiliation:

1. School of Information Science and Engineering, Changzhou University, Changzhou 213164, China

2. School of Information Engineering, Xuchang University, Xuchang 461000, China

3. College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

4. Department of Electronic Engineering, University of York, York, YO10 5DD, UK

Abstract

By coupling a diode bridge-based second-order memristor and an active voltage-controlled memristor with a capacitor, a three-element-based memristive circuit is synthesized and its system model is then built. The boundedness of the three-element-based memristive circuit is theoretically proved by employing the contraction mapping principle. Besides, the stability distributions of equilibrium points are theoretically and numerically expounded in a 2D parameter plane. The results imply the memristive circuit has a zero unstable saddle focus and a pair of nonzero stable node-foci or unstable saddle-foci depending on the considered parameters. The dynamical behaviors include point attractor, period, chaos, coexisting bifurcation mode, period-doubling bifurcation route, and crisis scenarios, which are explored using some common dynamical methods. Of particular concern, riddled attraction basins and multistability are uncovered under two sets of specified model parameters nearing the tiny neighborhood of crisis scenarios by local attraction basins and phase plane plots. The riddled attraction basins with island-like structure demonstrate that their dynamical behaviors are extremely sensitive to the initial conditions, resulting in the coexistence of limit cycles with period-2 and period-6, as well as the coexistence of period-1 limit cycles and single-scroll chaotic attractors. Moreover, a feasible on-breadboard hardware circuit is manually made and the experimental measurements are executed, upon which phase plane trajectories for some discrete model parameters are captured to further confirm the numerically simulated ones.

Funder

National Natural Science Foundation of China

Publisher

Hindawi Limited

Subject

Multidisciplinary,General Computer Science

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