Journal
MATHEMATICS
Volume 11, Issue 22, Pages -Publisher
MDPI
DOI: 10.3390/math11224641
Keywords
prey-taxis; nonlocal competition; numerical simulation; bifurcation; pattern formation
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This paper explores a predator-prey model that incorporates prey-taxis and a general functional response in a bounded domain. The stability, pattern formation, and global bifurcation of the model are examined. It is found that the inclusion of nonlocal terms enhances linear stability and can generate patterns due to prey-taxis. When the prey-tactic sensitivity is repulsive, a branch of nonconstant solutions emerges from the positive constant solution.
This paper will explore a predator-prey model that incorporates prey-taxis and a general functional response in a bounded domain. Firstly, we will examine the stability and pattern formation of both local and nonlocal models. Our main finding is that the inclusion of nonlocal terms enhances linear stability, and the system can generate patterns due to the effects of prey-taxis. Secondly, we consider the nonlinear prey-taxis as the bifurcation parameter in order to analyze the global bifurcation of this model. Specifically, we identify a branch of nonconstant solutions that emerges from the positive constant solution when the prey-tactic sensitivity is repulsive. Finally, we will validate the effectiveness of the theoretical conclusions using numerical simulation methods.
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