Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays
In this paper, a diffusive predator-prey system considering prey-taxis term with memory and maturation delays under Neumann boundary conditions is investigated. Firstly, the existence and stability of equilibria, especially the existence, uniqueness and stability of the positive equilibrium, are stu...
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University of Szeged
2024-08-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
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| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10909 |
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| _version_ | 1841533460333723648 |
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| author | Hongyan Sun Pengmiao Hao Jianzhi Cao |
| author_facet | Hongyan Sun Pengmiao Hao Jianzhi Cao |
| author_sort | Hongyan Sun |
| collection | DOAJ |
| description | In this paper, a diffusive predator-prey system considering prey-taxis term with memory and maturation delays under Neumann boundary conditions is investigated. Firstly, the existence and stability of equilibria, especially the existence, uniqueness and stability of the positive equilibrium, are studied. Secondly, we prove that: $\rm (i)$ there is no spatially homogeneous steady state bifurcation as the eigenvalue of the negative Laplace operator is zero; $\rm (ii)$ as this system is only with memory delay $\tau_{1}$, the the spatially nonhomogeneous Hopf bifurcation appears; $\rm (iii)$ when the model is only with maturation delay $\tau_{2}$, the system has spatially homogeneous and nonhomogeneous periodic solutions; $\rm (iv)$ for the case of two delays, the system has rich dynamics, for example, stability switches, whose curves have four forms. Finally, some numerical simulations are produced to verify and support the theoretical results. |
| format | Article |
| id | doaj-art-0bca68a54ac841c6ad1b6f9e5cf6890b |
| institution | Kabale University |
| issn | 1417-3875 |
| language | English |
| publishDate | 2024-08-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj-art-0bca68a54ac841c6ad1b6f9e5cf6890b2025-01-15T21:24:58ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752024-08-0120244012010.14232/ejqtde.2024.1.4010909Dynamics analysis of a diffusive prey-taxis system with memory and maturation delaysHongyan Sun0Pengmiao HaoJianzhi Cao1Hebei University, Baoding, PR ChinaHebei University, Baoding, PR ChinaIn this paper, a diffusive predator-prey system considering prey-taxis term with memory and maturation delays under Neumann boundary conditions is investigated. Firstly, the existence and stability of equilibria, especially the existence, uniqueness and stability of the positive equilibrium, are studied. Secondly, we prove that: $\rm (i)$ there is no spatially homogeneous steady state bifurcation as the eigenvalue of the negative Laplace operator is zero; $\rm (ii)$ as this system is only with memory delay $\tau_{1}$, the the spatially nonhomogeneous Hopf bifurcation appears; $\rm (iii)$ when the model is only with maturation delay $\tau_{2}$, the system has spatially homogeneous and nonhomogeneous periodic solutions; $\rm (iv)$ for the case of two delays, the system has rich dynamics, for example, stability switches, whose curves have four forms. Finally, some numerical simulations are produced to verify and support the theoretical results.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10909diffusive systemfear effectprey-taxismemory delaymaturation delay |
| spellingShingle | Hongyan Sun Pengmiao Hao Jianzhi Cao Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays Electronic Journal of Qualitative Theory of Differential Equations diffusive system fear effect prey-taxis memory delay maturation delay |
| title | Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays |
| title_full | Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays |
| title_fullStr | Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays |
| title_full_unstemmed | Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays |
| title_short | Dynamics analysis of a diffusive prey-taxis system with memory and maturation delays |
| title_sort | dynamics analysis of a diffusive prey taxis system with memory and maturation delays |
| topic | diffusive system fear effect prey-taxis memory delay maturation delay |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=10909 |
| work_keys_str_mv | AT hongyansun dynamicsanalysisofadiffusivepreytaxissystemwithmemoryandmaturationdelays AT pengmiaohao dynamicsanalysisofadiffusivepreytaxissystemwithmemoryandmaturationdelays AT jianzhicao dynamicsanalysisofadiffusivepreytaxissystemwithmemoryandmaturationdelays |