Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations

Zhijun LI; Siyuan FANG; Chengyi ZHOU

doi:10.11999/JEIT190855

Volume 42 Issue 4

Jun. 2020

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Zhijun LI, Siyuan FANG, Chengyi ZHOU. Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations[J]. Journal of Electronics & Information Technology, 2020, 42(4): 878-887. doi: 10.11999/JEIT190855

Citation:

Zhijun LI, Siyuan FANG, Chengyi ZHOU. Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations[J]. Journal of Electronics & Information Technology, 2020, 42(4): 878-887. doi: 10.11999/JEIT190855

Citation:

Zhijun LI, Siyuan FANG, Chengyi ZHOU. Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations[J]. Journal of Electronics & Information Technology, 2020, 42(4): 878-887. doi: 10.11999/JEIT190855

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Bursting Oscillations and Bifurcation Mechanism in Memristor-based Shimizu–Morioka System with Multi-frequency Slow Excitations

doi: 10.11999/JEIT190855

College of Information Engineering, Xiangtan University, Xiangtan, 411105, China

Funds: The National Natural Science Foundation of China (61471310), The National Key R&D Program of China (2018AAA0103300), The Natural Science Foundation of Hunan Province (2015JJ2142)

Received Date: 2019-11-01
Rev Recd Date: 2019-12-27

Available Online: 2020-01-07

Publish Date: 2020-06-04

Abstract

Abstract

In order to study the bursting oscillations and its formation mechanism of memristor-based system, a multi-timescale memristor-based S-M system is established by introducing a memristor device and two slowly changing periodic excitations into the Shimizu-Morioka (S-M) system. Firstly, the bursting behavior and bifurcation mechanism of S-M system under single excitation are studied, and a symmetric bursting pattern of “sub-Hopf/sub-Hopf” is obtained. Then the multi-frequency excitation system is transformed into single frequency excitation system by using De Moivre formula, and the influence of additional excitation amplitude and frequency on “sub Hopf / sub Hopf” bursting mode is analyzed by using the fast-slow analysis method. As a result, two new bursting patterns named as twisted “sub-Hopf/sub-Hopf” bursting and nested “sub-Hopf/sub-Hopf” are found under different amplitudes of the additional excitation. The corresponding bursting mechanisms are analyzed with time history diagram, bifurcation diagram and transformation phase diagram. Finally, Multisim simulation results, which are in good agreement with the numerical simulation results, are provided to verify the validity of the study.

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References(28)

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