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Title: | Global existence and stability of three species predator-prey system with prey-taxis | Authors: | Arumugam, G | Issue Date: | 2023 | Source: | Mathematical biosciences and engineering, 2023, v. 20, no. 5, p. 8448-8475 | Abstract: | In this paper, we study the following initial-boundary value problem of a three species predator-prey system with prey-taxis which describes the indirect prey interactions through a shared predator, i.e., under homogeneous Neumann boundary conditions in a bounded domain Ω ⊂ Rn(n ≧ 1) with smooth boundary, where the parameters d, η, r, µ, χ1, χ2, ai > 0, i = 1,..., 6. We first establish the global existence and uniform-in-time boundedness of solutions in any dimensional bounded domain under certain conditions. Moreover, we prove the global stability of the prey-only state and coexistence steady state by using Lyapunov functionals and LaSalle's invariance principle. | Keywords: | Global existence Global stabilization Local existence Predator-prey system Prey-taxis |
Publisher: | AIMS Press | Journal: | Mathematical biosciences and engineering | ISSN: | 1547-1063 | EISSN: | 1551-0018 | DOI: | 10.3934/mbe.2023371 | Rights: | ©2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0) The following publication Gurusamy Arumugam. Global existence and stability of three species predator-prey system with prey-taxis[J]. Mathematical Biosciences and Engineering, 2023, 20(5): 8448-8475 is available at https://doi.org/10.3934/mbe.2023371. |
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