Journal
MATHEMATICS
Volume 9, Issue 24, Pages -Publisher
MDPI
DOI: 10.3390/math9243193
Keywords
hunting cooperation; Allee effect; connecting orbit; invariant manifold; bifurcation; coexistence
Categories
Funding
- National Natural Science Foundation of China [11901369, 61872227, 11971281, 11771109]
- Natural Science Basic Research Plan in Shaanxi Province of China [2020JQ-699]
- Shandong Provincial Natural Science Foundation [ZR2019QA020]
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The paper investigates a diffusive predator-prey model with two delays, proving the existence of limit cycle in the weak cooperation model and identifying a loop of heteroclinic orbits connecting two equilibria by studying stable and unstable manifolds of saddles. When the conversion rate exceeds a threshold, both species go extinct.
This paper deals with a diffusive predator-prey model with two delays. First, we consider the local bifurcation and global dynamical behavior of the kinetic system, which is a predator-prey model with cooperative hunting and Allee effect. For the model with weak cooperation, we prove the existence of limit cycle, and a loop of heteroclinic orbits connecting two equilibria at a threshold of conversion rate p=p#, by investigating stable and unstable manifolds of saddles. When p > p#, both species go extinct, and when p
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