Abstract
In this paper, the influence of delayed feedback on the unified chaotic system from the Sprott C system and Yang system is studied. The Hopf bifurcation and dynamic behavior of the system are fully studied by using the central manifold theorem and bifurcation theory. The explicit formula, bifurcation direction, and stability of the periodic solution of bifurcation are given correspondingly. The Hopf bifurcation diagram and chaotic phenomenon are also analyzed by numerical simulation to prove the correctness of the theory. It shows that this delay control can only be applied to the hidden chaos with two stable equilibria.
Highlights
Since Lorentz inadvertently discovered chaos in a threedimensional autonomous system [1] in 1963, more and more scholars began to study the chaos of various systems
Due to the symmetry of the equilibrium point, we only study the Hopf bifurcation of E1 at τ τk
The properties of Hopf bifurcation are determined by the following parameters: ω2 determines the direction of Hopf bifurcation, β2 determines the stability of bifurcation periodic solutions, and T2 determines the period of bifurcation periodic solutions, and the specific values are shown as follows. e main theories and methods are from
Summary
Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Yulin 537000, Guangxi, China. E Hopf bifurcation and dynamic behavior of the system are fully studied by using the central manifold theorem and bifurcation theory. E explicit formula, bifurcation direction, and stability of the periodic solution of bifurcation are given correspondingly. E Hopf bifurcation diagram and chaotic phenomenon are analyzed by numerical simulation to prove the correctness of the theory. It shows that this delay control can only be applied to the hidden chaos with two stable equilibria
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