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Predator invasion in predator-prey model with prey-taxis in spatially heterogeneous environment

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS (2022)

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Summary: This paper analyzes the prey-predator models with indirect predator-taxis, where the chemical secreted by the predator triggers the repellent behavior of prey. The global existence and uniform boundedness of classical solutions up to two spatial dimensions are proved under the assumption of quadratic decay of predator. The linear stability analysis shows that large chemosensitivity gives rise to pattern formations, and global stability results for the nontrivial constant steady states are obtained through proper Lyapunov functionals.

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