Abstract
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.
Highlights
As we all know, Chua’s circuit is the first analog system to implement chaos in experiments
Chua et al expressed a conjecture that Andronov–Hopf bifurcation can lead to the birth of hidden attractors in Chua systems [19]
Based on the works mentioned above and the research about the Hopf bifurcations in [38], the modified Chua circuit system is described as the following form:
Summary
Chua’s circuit is the first analog system to implement chaos in experiments. Based on the works mentioned above and the research about the Hopf bifurcations in [38], the modified Chua circuit system is described as the following form: 3 Zero-Hopf bifurcation of system (2) It is easy to obtain the characteristic equation associated with the equilibrium E0 in Table 1: p(λ) = λ3 + (1 + bα + γ )λ2 + (–α + bα + β + γ + bαγ )λ + bαβ – αγ + bαγ = 0.
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