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Volume 2019, Article ID 6083853, 15 pages
Research Article

Dynamic Behaviors Analysis of a Chaotic Circuit Based on a Novel Fractional-Order Generalized Memristor

1State Key Laboratory Base of Eco-Hydraulic Engineering in Arid Area, Xi'an University of Technology, Xi'an 710048, China
2Institute of Water Resources and Hydroelectric Engineering, Xi'an University of Technology, Xi'an 710048, China
3College of Electronics and Information, Xi'an Polytechnic University, Xi'an 710048, China
4School of Electrical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Correspondence should be addressed to Shucan Cheng; nc.ude.tuax.uts@cnacuhs and Chaojun Wu; nc.ude.utjx.uts@uw.nujoahc

Received 29 January 2019; Revised 31 March 2019; Accepted 5 May 2019; Published 21 May 2019

Academic Editor: Honglei Xu

Copyright © 2019 Ningning Yang 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.


In this paper, a fractional-order chaotic circuit based on a novel fractional-order generalized memristor is proposed. It is proved that the circuit based on the diode bridge cascaded with fractional-order inductor has volt-ampere characteristics of pinched hysteresis loop. Then the mathematical model of the fractional-order memristor chaotic circuit is obtained. The impact of the order and system parameters on the dynamic behaviors of the chaotic circuit is studied by phase trajectory, Poincaré Section, and bifurcation diagram method. The order, as an important parameter, can increase the degree of freedom of the system. With the change of the order and parameters, the circuit will exhibit abundant dynamic behaviors such as coexisting upper and lower limit cycle, single scroll chaotic attractors, and double scroll chaotic attractors under different initial conditions. And the system exhibits antimonotonic behavior of antiperiodic bifurcation with the change of system parameters. The equivalent circuit simulations are designed to verify the results of the theoretical analysis and numerical simulation.