East Asian J. Appl. Math., 12 (2022), pp. 564-589.
Published online: 2022-04
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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} }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.