Predator-prey systems with defense switching and density-suppressed dispersal strategy
In this paper, we consider the following predator-prey system with defense switching mechanism and density-suppressed dispersal strategy $ \begin{equation*} \begin{cases} u_t = \Delta(d_1(w)u)+\frac{\beta_1 uvw}{u+v}-\alpha_1 u, & x\in \Omega, \; \; t>0, \\ v_t = \Delta(d_2(w...
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2022582?viewType=HTML |
| _version_ | 1818481756925329408 |
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| author | Jiawei Chu Hai-Yang Jin |
| author_facet | Jiawei Chu Hai-Yang Jin |
| author_sort | Jiawei Chu |
| collection | DOAJ |
| description | In this paper, we consider the following predator-prey system with defense switching mechanism and density-suppressed dispersal strategy
$ \begin{equation*} \begin{cases} u_t = \Delta(d_1(w)u)+\frac{\beta_1 uvw}{u+v}-\alpha_1 u, & x\in \Omega, \; \; t>0, \\ v_t = \Delta(d_2(w)v)+\frac{\beta_2 uvw}{u+v}-\alpha_2 v, & x\in \Omega, \; \; t>0, \\ w_t = \Delta w-\frac{\beta_3 uvw}{u+v}+\sigma w\left(1-\frac{w}{K}\right), & x\in \Omega, \; \; t>0, \\ \frac{\partial u}{\partial \nu} = \frac{\partial v}{\partial \nu} = \frac{\partial w}{\partial \nu} = 0, & x\in\partial\Omega, \; \; t>0, \\ (u, v, w)(x, 0) = (u_0, v_0, w_0)(x), & x\in\Omega, \ \end{cases} \end{equation*} $
where $ \Omega\subset{\mathbb{R}}^2 $ is a bounded domain with smooth boundary. Based on the method of energy estimates and Moser iteration, we establish the existence of global classical solutions with uniform-in-time boundedness. We further prove the global stability of co-existence equilibrium by using the Lyapunov functionals and LaSalle's invariant principle. Finally we conduct linear stability analysis and perform numerical simulations to illustrate that the density-suppressed dispersal may trigger the pattern formation. |
| first_indexed | 2024-12-10T11:39:18Z |
| format | Article |
| id | doaj.art-4061159cce9f46ac9f8157459e681a8e |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-10T11:39:18Z |
| publishDate | 2022-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-4061159cce9f46ac9f8157459e681a8e2022-12-22T01:50:18ZengAIMS PressMathematical Biosciences and Engineering1551-00182022-08-011912124721249910.3934/mbe.2022582Predator-prey systems with defense switching and density-suppressed dispersal strategyJiawei Chu0Hai-Yang Jin11. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong Kong, China2. School of Mathematics, South China University of Technology, Guangzhou 510640, ChinaIn this paper, we consider the following predator-prey system with defense switching mechanism and density-suppressed dispersal strategy $ \begin{equation*} \begin{cases} u_t = \Delta(d_1(w)u)+\frac{\beta_1 uvw}{u+v}-\alpha_1 u, & x\in \Omega, \; \; t>0, \\ v_t = \Delta(d_2(w)v)+\frac{\beta_2 uvw}{u+v}-\alpha_2 v, & x\in \Omega, \; \; t>0, \\ w_t = \Delta w-\frac{\beta_3 uvw}{u+v}+\sigma w\left(1-\frac{w}{K}\right), & x\in \Omega, \; \; t>0, \\ \frac{\partial u}{\partial \nu} = \frac{\partial v}{\partial \nu} = \frac{\partial w}{\partial \nu} = 0, & x\in\partial\Omega, \; \; t>0, \\ (u, v, w)(x, 0) = (u_0, v_0, w_0)(x), & x\in\Omega, \ \end{cases} \end{equation*} $ where $ \Omega\subset{\mathbb{R}}^2 $ is a bounded domain with smooth boundary. Based on the method of energy estimates and Moser iteration, we establish the existence of global classical solutions with uniform-in-time boundedness. We further prove the global stability of co-existence equilibrium by using the Lyapunov functionals and LaSalle's invariant principle. Finally we conduct linear stability analysis and perform numerical simulations to illustrate that the density-suppressed dispersal may trigger the pattern formation.https://www.aimspress.com/article/doi/10.3934/mbe.2022582?viewType=HTMLprey-predator systemdefense switchingdensity-suppressed diffusionglobal stabilitypattern formation |
| spellingShingle | Jiawei Chu Hai-Yang Jin Predator-prey systems with defense switching and density-suppressed dispersal strategy Mathematical Biosciences and Engineering prey-predator system defense switching density-suppressed diffusion global stability pattern formation |
| title | Predator-prey systems with defense switching and density-suppressed dispersal strategy |
| title_full | Predator-prey systems with defense switching and density-suppressed dispersal strategy |
| title_fullStr | Predator-prey systems with defense switching and density-suppressed dispersal strategy |
| title_full_unstemmed | Predator-prey systems with defense switching and density-suppressed dispersal strategy |
| title_short | Predator-prey systems with defense switching and density-suppressed dispersal strategy |
| title_sort | predator prey systems with defense switching and density suppressed dispersal strategy |
| topic | prey-predator system defense switching density-suppressed diffusion global stability pattern formation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2022582?viewType=HTML |
| work_keys_str_mv | AT jiaweichu predatorpreysystemswithdefenseswitchinganddensitysuppresseddispersalstrategy AT haiyangjin predatorpreysystemswithdefenseswitchinganddensitysuppresseddispersalstrategy |