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Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System

1
College of Electrical Engineering and Automation, Shandong University of Science and Technology, Qingdao 266590, China
2
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China
3
Department of Electronic Engineering, City University of Hong Kong, Hong Kong, China
*
Author to whom correspondence should be addressed.
Entropy 2019, 21(4), 415; https://doi.org/10.3390/e21040415
Received: 28 March 2019 / Revised: 16 April 2019 / Accepted: 16 April 2019 / Published: 19 April 2019
(This article belongs to the Section Complexity)
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Abstract

This paper reports the finding of unstable limit cycles and singular attractors in a two-dimensional dynamical system consisting of an inductor and a bistable bi-local active memristor. Inspired by the idea of nested intervals theorem, a new programmable scheme for finding unstable limit cycles is proposed, and its feasibility is verified by numerical simulations. The unstable limit cycles and their evolution laws in the memristor-based dynamic system are found from two subcritical Hopf bifurcation domains, which are subdomains of twin local activity domains of the memristor. Coexisting singular attractors are discovered in the twin local activity domains, apart from the two corresponding subcritical Hopf bifurcation domains. Of particular interest is the coexistence of a singular attractor and a period-2 or period-3 attractor, observed in numerical simulations. View Full-Text
Keywords: memristor; hopf bifurcation; unstable limit cycle; singular attractor; coexistence of attractors memristor; hopf bifurcation; unstable limit cycle; singular attractor; coexistence of attractors
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Chang, H.; Song, Q.; Li, Y.; Wang, Z.; Chen, G. Unstable Limit Cycles and Singular Attractors in a Two-Dimensional Memristor-Based Dynamic System. Entropy 2019, 21, 415.

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