中国物理B ›› 2022, Vol. 31 ›› Issue (6): 60502-060502.doi: 10.1088/1674-1056/ac539a

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

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The dynamics of a memristor-based Rulkov neuron with fractional-order difference

Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华)†, Quan-Li Deng(邓全利), and Cong Xu(徐聪)   

  1. College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
  • 收稿日期:2021-12-07 修回日期:2022-01-21 接受日期:2022-02-10 出版日期:2022-05-17 发布日期:2022-06-06
  • 通讯作者: Chun-Hua Wang E-mail:wch1227164@hnu.edu.cn
  • 基金资助:
    Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91964108), the National Natural Science Foundation of China (Grant No. 61971185), and the Natural Science Foundation of Hunan Province, China (Grant No. 2020JJ4218).

The dynamics of a memristor-based Rulkov neuron with fractional-order difference

Yan-Mei Lu(卢艳梅), Chun-Hua Wang(王春华)†, Quan-Li Deng(邓全利), and Cong Xu(徐聪)   

  1. College of Computer Science and Electronic Engineering, Hunan University, Changsha 410082, China
  • Received:2021-12-07 Revised:2022-01-21 Accepted:2022-02-10 Online:2022-05-17 Published:2022-06-06
  • Contact: Chun-Hua Wang E-mail:wch1227164@hnu.edu.cn
  • Supported by:
    Project supported by the Major Research Plan of the National Natural Science Foundation of China (Grant No. 91964108), the National Natural Science Foundation of China (Grant No. 61971185), and the Natural Science Foundation of Hunan Province, China (Grant No. 2020JJ4218).

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摘要： The exploration of the memristor model in the discrete domain is a fascinating hotspot. The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors. However, most of the current investigations are based on the integer-order discrete memristor, and there are relatively few studies on the form of fractional order. In this paper, a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator. Furthermore, the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor. The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph, the Lyapunov exponential spectrum, and the iterative graph. The results demonstrate that the fractional-order system has more abundant dynamics than the integer one, such as hyper-chaos, multi-stable and transient chaos. In addition, the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system. The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.

关键词: discrete memristor, Rulkov neuron, fractional-order difference, dynamics

Abstract: The exploration of the memristor model in the discrete domain is a fascinating hotspot. The electromagnetic induction on neurons has also begun to be simulated by some discrete memristors. However, most of the current investigations are based on the integer-order discrete memristor, and there are relatively few studies on the form of fractional order. In this paper, a new fractional-order discrete memristor model with prominent nonlinearity is constructed based on the Caputo fractional-order difference operator. Furthermore, the dynamical behaviors of the Rulkov neuron under electromagnetic radiation are simulated by introducing the proposed discrete memristor. The integer-order and fractional-order peculiarities of the system are analyzed through the bifurcation graph, the Lyapunov exponential spectrum, and the iterative graph. The results demonstrate that the fractional-order system has more abundant dynamics than the integer one, such as hyper-chaos, multi-stable and transient chaos. In addition, the complexity of the system in the fractional form is evaluated by the means of the spectral entropy complexity algorithm and consequences show that it is affected by the order of the fractional system. The feature of fractional difference lays the foundation for further research and application of the discrete memristor and the neuron map in the future.

Key words: discrete memristor, Rulkov neuron, fractional-order difference, dynamics

中图分类号:  (Low-dimensional chaos)

  • 05.45.Ac
05.45.-a (Nonlinear dynamics and chaos) 87.19.ll (Models of single neurons and networks) 05.45.Pq (Numerical simulations of chaotic systems)