Homoclinic bifurcation of a state feedback impulsive controlled prey–predator system with Holling-II functional response

  • Meng ZhangEmail author
  • Lansun Chen
  • Zeyu Li
Original paper


Keeping ecological balance between prey and predator population in ocean fishery is of great importance in fishery. A free developed two species prey–predator model with Holling-II functional response is carried out, and its fine case equilibrium is discussed. Then, the state feedback model which assumes the harvest of predator and supplement of prey as impulsive disturbance is presented to find the dynamical balance between prey and predator population. The existence of homoclinic cycle and order-1 periodic solution and the orbital asymptotical stability of the order-1 periodic solution are proved. Finally, some numerical simulations are displayed to confirm the results obtained in the paper.


State feedback Impulsive model Homoclinic bifurcation Order-1 periodic solution 



We would like to sincerely thank the reviewers for their careful reading and constructive opinions of the original manuscript.


This work is supported by NSFC (No. 11701026) and the Fundamental Research Funds for Beijing University of Civil Engineering and Architecture, China (X18225, X19031) for M. Zhang, NSFC (No. 11671346, No. 61751317) for L. Chen. M. Zhang would like to thank the China Scholarship Council for financial support of her overseas study(No. 201808110071).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of ScienceBeijing University of Civil Engineering and ArchitectureBeijingChina
  2. 2.Department of MathematicsPurdue UniversityWest LafayetteUSA
  3. 3.Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijingChina
  4. 4.Canvard CollegeBeijing Technology and Business UniversityBeijingChina

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