Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

doi:10.1007/s10483-015-2009-6

Applied Mathematics and Mechanics (English Edition) ›› 2015, Vol. 36 ›› Issue (12): 1639-1650.doi: https://doi.org/10.1007/s10483-015-2009-6

Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Shihui FU¹, Xiangying MENG², Qishao LU³

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2. Department of Biology, University of Maryland, College Park, MD 20742, U. S. A.;
3. Department of Dynamics and Control, Beihang University, Beijing 100191, China

收稿日期:2014-01-31 修回日期:2015-06-24 出版日期:2015-12-01 发布日期:2015-12-01
通讯作者: Qishao LU E-mail:qishaolu@hotmail.com
基金资助:
Project supported by the National Natural Science Foundation of China(Nos. U1204106, 11372282, 11272024, and 11371046) and the National Basic Research Program of China(973 Program)(Nos. 2012CB821200 and 2012CB821202)

Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Shihui FU¹, Xiangying MENG², Qishao LU³

1. School of Mathematics and Statistics, Zhengzhou University, Zhengzhou 450001, China;
2. Department of Biology, University of Maryland, College Park, MD 20742, U. S. A.;
3. Department of Dynamics and Control, Beihang University, Beijing 100191, China

Received:2014-01-31 Revised:2015-06-24 Online:2015-12-01 Published:2015-12-01
Contact: Qishao LU E-mail:qishaolu@hotmail.com
Supported by:
Project supported by the National Natural Science Foundation of China(Nos. U1204106, 11372282, 11272024, and 11371046) and the National Basic Research Program of China(973 Program)(Nos. 2012CB821200 and 2012CB821202)

摘要/Abstract

摘要： Chua's circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua's circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the supercritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous(PWSC) systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. Therefore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.

关键词: modified Chua's circuit, stability, boundary equilibrium point, bifurcation

Abstract: Chua's circuit is a well-known nonlinear electronic model, having complicated nonsmooth dynamic behaviors. The stability and boundary equilibrium bifurcations for a modified Chua's circuit system with the smooth degree of 3 are studied. The parametric areas of stability are specified in detail. It is found that the bifurcation graphs of the supercritical and irregular pitchfork bifurcations are similar to those of the piecewise-smooth continuous(PWSC) systems caused by piecewise smoothness. However, the bifurcation graph of the supercritical Hopf bifurcation is similar to those of smooth systems. Therefore, the boundary equilibrium bifurcations of the non-smooth systems with the smooth degree of 3 should receive more attention due to their special features.

Key words: modified Chua's circuit, bifurcation, boundary equilibrium point, stability

中图分类号:

O361.3

Shihui FU, Xiangying MENG, Qishao LU. Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(12): 1639-1650.

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Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

Stability and boundary equilibrium bifurcations of modified Chua's circuit with smooth degree of 3

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