Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis
We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of...
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| Format: | Article |
| Language: | English |
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AIMS Press
2021-08-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2021331?viewType=HTML |
| _version_ | 1828144847642427392 |
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| author | Yong Luo |
| author_facet | Yong Luo |
| author_sort | Yong Luo |
| collection | DOAJ |
| description | We study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey). |
| first_indexed | 2024-04-11T20:23:17Z |
| format | Article |
| id | doaj.art-fa2e524b46704f13a3a6e9f870e34844 |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-04-11T20:23:17Z |
| publishDate | 2021-08-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-fa2e524b46704f13a3a6e9f870e348442022-12-22T04:04:46ZengAIMS PressMathematical Biosciences and Engineering1551-00182021-08-011856672669910.3934/mbe.2021331Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxisYong Luo0Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Hong KongWe study the existence of global unique classical solution to a density-dependent prey-predator population system with indirect prey-taxis effect. With two Lyapunov functions appropriately constructed, we then show that the solution can asymptotically approach prey-only state or coexistence state of the system under suitable conditions. Moreover, linearized analysis on the system at these two constant steady states shows their linear instability criterion. By numerical simulation we find that some density-dependent prey-taxis and predators' diffusion may either flatten the spatial one-dimensional patterns which exist in non-density-dependent case, or break the spatial two-dimensional distribution similarity which occurs in non-density-dependent case between predators and chemoattractants (released by prey).https://www.aimspress.com/article/doi/10.3934/mbe.2021331?viewType=HTMLdensity-dependentindirect prey-taxislyapunov functionasymptotical stabilitynonlinear semigroup |
| spellingShingle | Yong Luo Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis Mathematical Biosciences and Engineering density-dependent indirect prey-taxis lyapunov function asymptotical stability nonlinear semigroup |
| title | Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis |
| title_full | Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis |
| title_fullStr | Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis |
| title_full_unstemmed | Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis |
| title_short | Global existence and stability of the classical solution to a density-dependent prey-predator model with indirect prey-taxis |
| title_sort | global existence and stability of the classical solution to a density dependent prey predator model with indirect prey taxis |
| topic | density-dependent indirect prey-taxis lyapunov function asymptotical stability nonlinear semigroup |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2021331?viewType=HTML |
| work_keys_str_mv | AT yongluo globalexistenceandstabilityoftheclassicalsolutiontoadensitydependentpreypredatormodelwithindirectpreytaxis |