Fractals analysis and control for a kind of three-species ecosystem with symmetrical coupled predatory behavior

Abstract

The Lotka-Volterra model plays an important role in the research area of population biology. This work presents the analysis of dynamical behaviours of a kind of three species GLV system
from the viewpoint of fractals. The definition of Julia set which describes the initial distribution of the three species’ densities is introduced. Then a gradient control method which contains both giant parameter and state feedback is applied to realize the control of Julia set. Coupling terms are designed to realize the synchronization of two Julia sets. Numerical examples are included to verify the conclusions