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Chin. Phys. B, 2021, Vol. 30(12): 120515    DOI: 10.1088/1674-1056/ac1fdf
Special Issue: SPECIAL TOPIC— Interdisciplinary physics: Complex network dynamics and emerging technologies
SPECIAL TOPIC—Interdisciplinary physics: Complex network dynamics and emerging technologies Prev   Next  

Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation

Zong-Li Yang(杨宗立)1, Dong Liang(梁栋)1,2,†, Da-Wei Ding(丁大为)1,2,‡, Yong-Bing Hu(胡永兵)1, and Hao Li(李浩)3
1 School of Electronics and Information Engineering, Anhui University, Hefei 230601, China;
2 National Engineering Research Center for Agro-Ecological Big Data Analysis & Application, Anhui University, Hefei 230601, China;
3 State Grid Lu'an Electric Power Supply Company, Lu'an 237006, China
Abstract  This paper proposes a fractional-order simplest chaotic system using a bi-stable locally-active memristor. The characteristics of the memristor and transient transition behaviors of the proposed system are analyzed, and this circuit is implemented digitally using ARM-based MCU. Firstly, the mathematical model of the memristor is designed, which is nonvolatile, locally-active and bi-stable. Secondly, the asymptotical stability of the fractional-order memristive chaotic system is investigated and some sufficient conditions of the stability are obtained. Thirdly, complex dynamics of the novel system are analyzed using phase diagram, Lyapunov exponential spectrum, bifurcation diagram, basin of attractor, and coexisting bifurcation, coexisting attractors are observed. All of these results indicate that this simple system contains the abundant dynamic characteristics. Moreover, transient transition behaviors of the system are analyzed, and it is found that the behaviors of transient chaotic and transient period transition alternately occur. Finally, the hardware implementation of the fractional-order bi-stable locally-active memristive chaotic system using ARM-based STM32F750 is carried out to verify the numerical simulation results.
Keywords:  fractional calculus      bi-stable locally-active memristor      transient transition behaviors      ARM implementation  
Received:  23 June 2021      Revised:  29 July 2021      Accepted manuscript online:  22 August 2021
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  45.10.Hj (Perturbation and fractional calculus methods)  
  47.10.Fg (Dynamical systems methods)  
Corresponding Authors:  Dong Liang, Da-Wei Ding     E-mail:;

Cite this article: 

Zong-Li Yang(杨宗立), Dong Liang(梁栋), Da-Wei Ding(丁大为), Yong-Bing Hu(胡永兵), and Hao Li(李浩) Transient transition behaviors of fractional-order simplest chaotic circuit with bi-stable locally-active memristor and its ARM-based implementation 2021 Chin. Phys. B 30 120515

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