Fractal analysis and control in the predator–prey model

Abstract

ABSTRACTThe two-dimensional predator–prey Lotka–Volterra model is discussed from the point of fractal theory. Julia set of the discrete version of the model is introduced. Then, the linear feedback control is taken to control the Julia set. By controlling the Julia set, the attractive domain of the attractive fixed point is controlled indirectly. To associate two different Julia sets of the model with different parameters, nonlinear coupling items are designed to make one Julia set change to be another. The simulations illustrate the efficacy of these methods.