JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (7): 73-81.doi: 10.6040/j.issn.1671-9352.0.2020.496

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Stability and Turing instability of a predator-prey reaction-diffusion system with schooling behavior

ZHOU Yan, ZHANG Cun-hua*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2021-07-19

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Abstract: A predator-prey reaction-diffusion system of fish with schooling behavior is considered. By analyzing the distribution of the roots of the characteristic equation of the linearized system at the unique constant positive equilibrium solution in the complex plane in detail, the stability and the Turing instability of the unique positive equilibrium solution of the system are discussed. In addition,the obtained theoretical conclusions are verified numerically by MATLAB software.

Key words: schooling behavior, predator-prey reaction-diffusion system, stability, Turing instability

CLC Number: 

  • O175.2
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