A New Method for Control Chaos Based on Delay Feeback of System Variables

Abstract

A new method for control chaos based on delay feedback of system variables is proposed. The control results of three typical chaotic systems are given. The method of control chaos can be easily realized in physical systems, for the control price of this method is low. The mechanism of the method is also discussed based on varied of average value of Lyapunov function.

Adaptive control of bifurcation and chaos in a time-delayed system

“…Hence, the task of controlling oscillations in time-delayed systems using the chaos and bifurcation control strategies is of great importance in a diverse range of applications such as inertial two-neuron systems, oncolytic virus dynamics, small-world networks, cellular neural networks, and so on. [4][5][6][7][8][9][10] From the viewpoint of the control strategy, the developed methods can be classified into two main categories: feedback control methods [11][12][13] in which feedback strategies are applied to control bifurcation and chaos, and non-feedback control methods [14][15][16] in which bifurcation and chaos are suppressed by applying weak periodic perturbations or parameter perturbations. Based on these works, a hybrid control strategy [17,18] is proposed, in which the parameter perturbation and the state feedback are combined to control the period-doubling bifurcation and chaos.…”

Equilibrium points and bifurcation control of a chaotic system

“…The first one is based on a feedback control strategy, such as by Ott, Grebogi, Yorke (OGY), [2,3] state space feedback control. [4] The second one is based on non-feedback control strategy, [5,6] for instance, the entrainment and migration control method. [7,8] However, it is difficult to guarantee the stability in the control process via the second method.…”