忆容振荡器初值切换调控的超级多稳定性及其机理分析

陈蓓; 徐权; 陈墨; 武花干; 包伯成

doi:10.1631/FITEE.2000622

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忆容振荡器初值切换调控的超级多稳定性及其机理分析

常规文章 | Updated：2022-06-06

- 忆容振荡器初值切换调控的超级多稳定性及其机理分析
- Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator
- 信息与电子工程前沿（英文） 2021年22卷第11期页码：1517-1531
- Affiliations：
  
  School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
- Author bio：
  
  Bocheng BAO, E-mail: mervinbao@126.com
- Funds：
  
  Project supported by the National Natural Science Foundation of China (Nos. 51777016 and 61801054), the Natural Science Foundation of Jiangsu Province, China (No. BK20191451), the Natural Science Foundation of Changzhou, Jiangsu Province, China (No. CJ20190037), and the Open Research Fund of Key Laboratory of MEMS of Ministry of Education, Southeast University, China
- DOI：10.1631/FITEE.2000622
  中图分类号： O415
- 收稿：2020-09-09，
  
  修回：2021-;9-30，
  
  纸质出版：2021-11
- Accepted：
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陈蓓, 徐权, 陈墨, 等. 忆容振荡器初值切换调控的超级多稳定性及其机理分析[J]. 信息与电子工程前沿（英文）, 2021,22(11):1517-1531.

Bei CHEN, Quan XU, Mo CHEN, et al. Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(11): 1517-1531.
陈蓓, 徐权, 陈墨, 等. 忆容振荡器初值切换调控的超级多稳定性及其机理分析[J]. 信息与电子工程前沿（英文）, 2021,22(11):1517-1531. DOI： 10.1631/FITEE.2000622.

Bei CHEN, Quan XU, Mo CHEN, et al. Initial-condition-switched boosting extreme multistability and mechanism analysis in a memcapacitive oscillator[J]. Frontiers of Information Technology & Electronic Engineering, 2021, 22(11): 1517-1531. DOI： 10.1631/FITEE.2000622.

摘要

超级多稳定性以其丰富多样的动力学状态和工程应用中的极大灵活性受到科学家们关注。利用4个线性电路元件和一个具有余弦逆忆容值的非线性荷控型忆容元件，构造了一个四维忆容振荡器。四维忆容振荡器具有一个线平衡集，其稳定性随忆容的初始条件周期性演化。由于周期性演化的稳定性，四维忆容振荡器展现了初值切换调控的超级多稳定性。通过分岔图、李雅普诺夫指数和相轨图，揭示了周期倍增/减半分岔、混沌危机和初值切换共存吸引子的复杂动力学行为。在此基础上，通过积分变换得到一个重构系统，揭示了忆容振荡器中初值切换调控超级多稳定性的形成机理。最后设计了重构系统的实现电路，并进行了PSIM电路仿真，验证了数值分析的有效性。

Abstract

Extreme multistability has seized scientists' attention due to its rich diversity of dynamical behaviors and great flexibility in engineering applications. In this paper

a four-dimensional (4D) memcapacitive oscillator is built using four linear circuit elements and one nonlinear charge-controlled memcapacitor with a cosine inverse memcapacitance. The 4D memcapacitive oscillator possesses a line equilibrium set

and its stability periodically evolves with the initial condition of the memcapacitor. The 4D memcapacitive oscillator exhibits initial-condition-switched boosting extreme multistability due to the periodically evolving stability. Complex dynamical behaviors of period doubling/halving bifurcations

chaos crisis

and initial-condition-switched coexisting attractors are revealed by bifurcation diagrams

Lyapunov exponents

and phase portraits. Thereafter

a reconstructed system is derived via integral transformation to reveal the forming mechanism of the initial-condition-switched boosting extreme multistability in the memcapacitive oscillator. Finally

an implementation circuit is designed for the reconstructed system

and Power SIMulation (PSIM) simulations are executed to confirm the validity of the numerical analysis.

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