JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (10): 43-53.doi: 10.6040/j.issn.1671-9352.0.2022.308

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Dynamics of a reaction-diffusion predator-prey model incorporating prey refuge and fear effect

Qian CAO1(),Yanling LI2,*(),Weihua SHAN1   

  1. 1. School of Science, Chang'an University Xi'an 710064, Shaanxi, China
    2. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119, Shaanxi, China
  • Received:2022-05-30 Online:2023-10-20 Published:2023-10-17
  • Contact: Yanling LI E-mail:mathcq19@chd.edu.cn;yanlingl@snnu.edu.cn

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Abstract:

For a reaction-diffusion predator-prey system with prey refuge and fear effect, the Turing instability of the positive constant solution for the system and a priori estimates of solutions for the system are investigated. It is proved that there is no nonconstant positive steady-state solution for the system under certain parameter conditions. Moreover, taking the diffusion coefficient of the predator as the bifurcation parameter, the global structure of the bifurcation solution is constructed. It is found that the bifurcation solution can be extended to infinity when the diffusion coefficient of predator is greater than some critical value. Finally, by numerical simulations, the theoretical results are verified and supplemented.

Key words: Turing instability, bifurcation theory, prey refuge, fear effect, reaction-diffusion predator-prey model

CLC Number: 

  • O175

Fig.1

Spatio-temporal patterns generated by the system (1) for $d_{2}=1<\tilde{d}_{2}$"

Fig.2

Spatio-temporal patterns generated by the system (1) for $d_{2}=500>\tilde{d}_{2}$"

Fig.3

Spatio-temporal patterns generated by the system (1) for d1=0.1"

Fig.4

Spatio-temporal patterns generated by the system (1) for m=0"

Fig.5

Spatio-temporal patterns generated by the system (1) for k=0, d1=0.01 and d2=500"

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