Effective Control and Bifurcation Analysis in a Chaotic System with Distributed Delay Feedback

Abstract EN

We discuss the dynamic behavior of a new Lorenz-like chaotic system with distributed delayed feedback by the qualitative analysis and numerical simulations.

It is verified that the equilibria are locally asymptotically stable when α ∈ ( 0 , α 0 ) and unstable when α ∈ ( α 0 , ∞ ) ; Hopf bifurcation occurs when α crosses a critical value α 0 by choosing α as a bifurcation parameter.

Meanwhile, the explicit algorithm for determining the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions is derived by normal form theorem and center manifold argument.

Furthermore, regarding α as a bifurcation parameter, we explore variation tendency of the dynamics behavior of a chaotic system with the increase of the parameter value α .