TY - JOUR
T1 - Stability Analysis of a Diffusive Predator-Prey Model with Hunting Cooperation
AU - Wu , Shuhao
AU - Song , Yongli
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 321
EP - 334
PY - 2021
DA - 2021/04
SN - 3
DO - http://doi.org/10.12150/jnma.2021.321
UR - https://global-sci.org/intro/article_detail/jnma/18793.html
KW - Predator-prey model, Hunting cooperation, Stability, Turing bifurcation.
AB - <p style="text-align: justify;">In this paper, we are concerned with the dynamics of a diffusive predator-prey model that incorporates the functional response concerning hunting cooperation. First, we investigate the stability of the semi-trivial steady state. Then, we investigate the influence of the diffusive rates on the stability of the positive constant steady state. It is shown that there exists diffusion-driven Turing instability when the diffusive rate of the predator is smaller than the critical value, which is dependent on the diffusive rate of the prey, and the semi-trivial steady state and the positive constant steady state are both locally asymptotically stable when the diffusive rate of the predator is larger than the critical value. Finally, the nonexistence of nonconstant steady states is discussed.</p>