Fractal dimension analysis and control of Julia set generated by fractional Lotka–Volterra models

Abstract

This paper reports the investigation of a fractional Lotka–Volterra model from the fractal viewpoint. The fractal characteristic of the Julia set is discussed after introducing the discrete version of this model. Then, control of the model’s Julia set is studied via two different control strategies. Numerical simulations are presented to further verify the correctness and effectiveness of the main theoretical results.