Stabilization in chaotic maps using hybrid chaos control procedure

Abstract

Much attention have been devoted to control of chaos in nonlinear system in the last few decades and several control procedures have been derived to find the stability target in difference and differential equations. In this study, a novel hybrid chaos control procedure is derived which allows to stabilize the chaos in most accepted discrete chaotic equations of population growth models about the globally accepted stable equilibrium. Since the system depends on the parameters κ, α, and r, the chaos in the given system may be stabilized in different fixed points states of order p, when it is kicked with the parameter κ. From this point of view, the procedure is simple, flexible, and gives the advantage to take the numerous parameter values to reach the demanded stability in periodic states of order p. This hybrid approach to control makes it novel as compared to existing methods. Further, we provide the geometrical interpretation followed by a few examples, control curves, bifurcation plots, time-series plots, and Lyapunov exponent to illustrate our numerical results.