Control of Divergence in an Extended Invertible Logistic Map

Abstract

The extended invertible Logistic map and its properties are investigated in this paper. It is demonstrated that initial conditions of the extended invertible Logistic map can yield trajectories of three different types. Dedicated algorithms are used to prove the existence of transient Wada-type boundaries in the phase plane of initial conditions. An adaptive control technique for the temporary control of the divergence of the extended invertible Logistic map is proposed. This control technique is based on short impulses and exploits the properties of the Wada-type boundaries. Computational experiments are used to illustrate the efficacy of the proposed technique.