Volume 12, Issue 3
Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis

East Asian J. Appl. Math., 12 (2022), pp. 564-589.

Published online: 2022-04

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• Abstract

This paper considers the global existence and boundedness of classical solutions to a predator-prey-mutualist model with prey-taxis. In addition, by constructing the Lyapunov functionals, we proved when $\alpha < (ac/b)·r +a/b,$ the positive equilibrium point is globally asymptotic stable; and when $\alpha \in ((ac/b)·r + a/b, M_1),$ the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical examples to validate our results.

• Keywords

Chemotaxis, predator-prey-mutualist, boundedness, stabilization.

35A01, 35B40, 35J57, 35Q92

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@Article{EAJAM-12-564, author = {}, title = {Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis}, journal = {East Asian Journal on Applied Mathematics}, year = {2022}, volume = {12}, number = {3}, pages = {564--589}, abstract = {

This paper considers the global existence and boundedness of classical solutions to a predator-prey-mutualist model with prey-taxis. In addition, by constructing the Lyapunov functionals, we proved when $\alpha < (ac/b)·r +a/b,$ the positive equilibrium point is globally asymptotic stable; and when $\alpha \in ((ac/b)·r + a/b, M_1),$ the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical examples to validate our results.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.220421.280921}, url = {http://global-sci.org/intro/article_detail/eajam/20407.html} }
TY - JOUR T1 - Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis JO - East Asian Journal on Applied Mathematics VL - 3 SP - 564 EP - 589 PY - 2022 DA - 2022/04 SN - 12 DO - http://doi.org/10.4208/eajam.220421.280921 UR - https://global-sci.org/intro/article_detail/eajam/20407.html KW - Chemotaxis, predator-prey-mutualist, boundedness, stabilization. AB -

This paper considers the global existence and boundedness of classical solutions to a predator-prey-mutualist model with prey-taxis. In addition, by constructing the Lyapunov functionals, we proved when $\alpha < (ac/b)·r +a/b,$ the positive equilibrium point is globally asymptotic stable; and when $\alpha \in ((ac/b)·r + a/b, M_1),$ the semi-trivial equilibrium point is globally asymptotic stable. Finally, we give some numerical examples to validate our results.

Qian Zhao & Bin Liu. (2022). Global Existence and Asymptotic Behavior in a Predator-Prey-Mutualist Model with Prey-Taxis. East Asian Journal on Applied Mathematics. 12 (3). 564-589. doi:10.4208/eajam.220421.280921
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