Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system

Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium points of the modified Chua circuit system. B...

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Bibliographic Details
Published in:Advances in difference equations 2018-04, Vol.2018 (1), p.1-17, Article 141
Main Authors: Li, Junze, Liu, Yebei, Wei, Zhouchao
Format: Article
Language:English
Subjects:
Analysis
Bifurcation theory
Chua’s circuit system
Circuits
Classical Hopf bifurcation
Difference and Functional Equations
Economic models
Electronic circuits
Functional Analysis
Hopf bifurcation
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Periodic solution
Thermal energy
Zero-Hopf bifurcation
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Summary:Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium points of the modified Chua circuit system. By using the averaging theory, we consider zero-Hopf bifurcation of the modified Chua system. Moreover, the existence of periodic solutions in the modified Chua system is derived from the classical Hopf bifurcation theorem.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/s13662-018-1597-8