Acta mathematica scientia,Series A ›› 2019, Vol. 39 ›› Issue (4): 951-962.

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Fractal Feature and Control of Three-Species Predator-Prey Model

Changxu Shao,Shutang Liu*()   

  1. School of Control Science and Engineering, Shandong University, Jinan 250061
  • Received:2018-06-07 Online:2019-08-26 Published:2019-09-11
  • Contact: Shutang Liu
  • Supported by:
    the Key Program of National Natural Science Foundation(61533011)


The law of population quantity change is one of the key problems in Animal Ecology and Resource Management. By studying the change of population quantity, we can effectively grasp the population dynamics and living habits, which is of great significance for the rational utilization of resources and the protection of ecology. In this paper, we discuss the three-species predator-prey model from the point of fractal theory. We construct the Julia set of 3D predatorprey model. By studying the property of Julia sets, we discuss the conditions for the model to be stable, and take feedback control terms to realize the transformation from instability to stability. In addition, the effects of single population changes on the other two populations and ecosystems were analyzed. Finally, the nonlinear coupling terms with different parameters are constructed, the response system is transformed into the target system, and the synchronization between different systems is realized. Simulation results show the effectiveness of the method.

Key words: Predator-prey model, Stability, Julia set, Feedback control, Synchronization

CLC Number: 

  • O29