Abstract
We choose the delay as a variable parameter and investigate the Lorentz-like system with delayed feedback by using Hopf bifurcation theory and functional differential equations. The local stability of the positive equilibrium and the existence of Hopf bifurcations are obtained. After that the direction of Hopf bifurcation and stability of periodic solutions bifurcating from equilibrium is determined by using the normal form theory and center manifold theorem. In the end, some numerical simulations are employed to validate the theoretical analysis. The results show that the purpose of controlling chaos can be achieved by adjusting appropriate feedback effect strength and delay parameters. The applied delay feedback control method in this paper is general and can be applied to other nonlinear chaotic systems.
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