The chaotic control on the occasional nonlinear time-delayed feedback

The method of controlling chaos by occasional nonlinear time-delayed feedback is proposed. Through the numerical analysis of bifurcation diagram and Lyapunov exponent, we found that the systematic chaos can be controlled effectively by the nonlinear time-delayed feedback as the form of u(x(n),x(n-k)) = cx(n)x(n-k). Under the proper feedback coefficient c, time-delayed coefficient k and occasional feedback period N, the system could be controlled from chaos to the steady periodic orbit, and also the steady period is the integral multiple of the occasional feedback period N.