Electron. J. Differential Equations, Vol. 2020 (2020), No. 36, pp. 1-14.
Dynamics and pattern formation in diffusive predator-prey models with predator-taxis
Zhongyuan Sun, Jinfeng Wang
Abstract:
We consider a three-species predator-prey system in which the predator has a stage
structure and the prey moves to avoid the mature predator, which is called the
predator-taxis. We obtain the existence and uniform-in-time boundedness of
classical global solutions for the model in any dimensional bounded domain
with the Neumann boundary conditions.
If the attractive predator-taxis coefficient is under a critical value,
the homogenerous positive steady state maintains its stability.
Otherwise, the system may generate Hopf bifurcation solutions.
Our results suggest that the predator-taxis amplifies the spatial heterogeneity of
the three-species predator-prey system, which is different from the effect of that
in two-species predator-prey systems.
Submitted December 25, 2019. Published April 23, 2020.
Math Subject Classifications: 35K57, 35K59, 92D25
Key Words: Predator-prey; predator-taxis' global solution; spatial pattern.
DOI: 10.58997/ejde.2020.36
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Zhongyuan Sun
School of Mathematics Sciences and
Y. Y. Tseng Functional Analysis Research Center
Harbin Normal University
Harbin, Heilongjiang, 150001, China
email: zhongyuansunmath@163.com
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Jinfeng Wang
School of Mathematics Sciences and
Y. Y. Tseng Functional Analysis Research Center
Harbin Normal University
Harbin, Heilongjiang, 150001, China
email: jinfengwangmath@163.com
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