Controlling the period-doubling bifurcation of logistic model

Abstract

The bifurcation control of period-doubling bifurcation in logistic model have been studied in this paper. The bifurcation maps of logistic model are achieved and the bifurcation characteristic of the dynamical system is changed by using variable-parameter linear controllers. In order to change the parameter value of all existing bifurcation points and modify the shape of a bifurcation chain, we can design variable controllers in for practical aims. Moreover, the bifurcation map may be obtained more effectively by adequately choosing the controller gain.