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

doi:10.1088/1674-1056/ac1fdf

中国物理B ›› 2021, Vol. 30 ›› Issue (12): 120515-120515.doi: 10.1088/1674-1056/ac1fdf

所属专题： SPECIAL TOPIC — Interdisciplinary physics: Complex network dynamics and emerging technologies

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

收稿日期:2021-06-23 修回日期:2021-07-29 接受日期:2021-08-22 出版日期:2021-11-15 发布日期:2021-11-25
通讯作者: Dong Liang, Da-Wei Ding E-mail:07115@ahu.edu.cn;dwding@ahu.edu.cn

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

Received:2021-06-23 Revised:2021-07-29 Accepted:2021-08-22 Online:2021-11-15 Published:2021-11-25
Contact: Dong Liang, Da-Wei Ding E-mail:07115@ahu.edu.cn;dwding@ahu.edu.cn

摘要/Abstract

摘要： 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.

关键词: fractional calculus, bi-stable locally-active memristor, transient transition behaviors, ARM implementation

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.

Key words: fractional calculus, bi-stable locally-active memristor, transient transition behaviors, ARM implementation

中图分类号: (Nonlinear dynamics and chaos)

05.45.-a

45.10.Hj (Perturbation and fractional calculus methods) 47.10.Fg (Dynamical systems methods)

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[J]. 中国物理B, 2021, 30(12): 120515-120515.

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

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

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