Chaotic control of Hénon map with feedback and nonfeedback methods

In this paper, based on the stability theorem of discrete systems and the idea of less energy, which means more stability in physical systems, feedback and nonfeedback methods are used, respectively to stabilize chaotic Hénon map at different p-periodic orbits. The two methods are compared in different aspects. Numerical simulations show the feasibility and effectiveness of them.

Research highlights
► Avoiding the lack of a great deal of mathematical analysis and computation in the feedback method reported in this paper or literatures, a minimum energy approach is proposed.
► The minimum energy approach which is more easy to implement is applied to chaotic control via stabilizing a classic discrete system, Hénon map at different p-periodic orbits.
► The simulation results show the effectiveness of the method.