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Complexity
Volume 2019, Article ID 2051053, 13 pages
https://doi.org/10.1155/2019/2051053
Research Article

Complex Dynamical Behaviors of a Fractional-Order System Based on a Locally Active Memristor

1Aliyun School of Big Data, Changzhou University, Changzhou 213164, China
2College of Automation Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
3Institute of Advanced Technology, Nanjing University of Posts and Telecommunications, Nanjing 210042, China
4School of Information Science and Engineering, Changzhou University, Changzhou 213164, China
5Mechatronics, Embedded Systems and Automation Lab, School of Engineering, University of California, Merced, Merced, CA 95343, USA

Correspondence should be addressed to Bocheng Bao; nc.ude.uzcc@cboab

Received 10 May 2019; Revised 30 August 2019; Accepted 8 October 2019; Published 20 November 2019

Guest Editor: Lazaros Moysis

Copyright © 2019 Yajuan Yu et al. 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.

Abstract

A fractional-order locally active memristor is proposed in this paper. When driven by a bipolar periodic signal, the generated hysteresis loop with two intersections is pinched at the origin. The area of the hysteresis loop changes with the fractional order. Based on the fractional-order locally active memristor, a fractional-order memristive system is constructed. The stability analysis is carried out and the stability conditions for three equilibria are listed. The expression of the fractional order related to Hopf bifurcation is given. The complex dynamical behaviors of Hopf bifurcation, period-doubling bifurcation, bistability and chaos are shown numerically. Furthermore, the bistability behaviors of the different fractional order are validated by the attraction basins in the initial value plane. As an alternative to validating our results, the fractional-order memristive system is implemented by utilizing Simulink of MATLAB. The research results clarify that the complex dynamical behaviors are attributed to two facts: one is the fractional order that affects the stability of the equilibria, and the other is the local activeness of the fractional-order memristor.