Control of Julia sets of the complex Henon system

In the complicated weather behavior, Lorenz system is an important model in the research of the convection processes in the atmosphere. The same basic properties of Lorenz system can be observed in the discrete Henon map which is a two-dimensional dynamical system. It is necessary to study and control the Julia sets of the complex Henon map, since the complex variable Henon map depicts some complicated behaviors and Julia set is an important notion to describe these phenomena. In this paper, the gradient control method and the auxiliary reference feedback control method are taken on the Julia sets of the two dimensional complex Henon system.