Spatio-temporal Bazykin’s model with space-time nonlocality
This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis dete...
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| Format: | Article |
| Language: | English |
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AIMS Press
2020-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2020262?viewType=HTML |
| _version_ | 1818590480931225600 |
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| author | Swadesh Pal Malay Banerjee Vitaly Volpert |
| author_facet | Swadesh Pal Malay Banerjee Vitaly Volpert |
| author_sort | Swadesh Pal |
| collection | DOAJ |
| description | This work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state. |
| first_indexed | 2024-12-16T09:57:13Z |
| format | Article |
| id | doaj.art-6cef6918eb244dd9907e68bf4a58275a |
| institution | Directory Open Access Journal |
| issn | 1551-0018 |
| language | English |
| last_indexed | 2024-12-16T09:57:13Z |
| publishDate | 2020-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj.art-6cef6918eb244dd9907e68bf4a58275a2022-12-21T22:35:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182020-07-011754801482410.3934/mbe.2020262Spatio-temporal Bazykin’s model with space-time nonlocalitySwadesh Pal 0Malay Banerjee 1Vitaly Volpert21. Department of Mathematics & Statistics, IIT Kanpur, Kanpur, 208016, India1. Department of Mathematics & Statistics, IIT Kanpur, Kanpur, 208016, India2. Institut Camille Jordan, UMR 5208 CNRS, University Lyon 1, 69622 Villeurbanne, France 3. INRIA, Team Dracula, INRIA Lyon La Doua, 69603 Villeurbanne, France 4. Peoples’ Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya St, Moscow, 117198, RussiaThis work deals with a reaction-diffusion model for prey-predator interaction with Bazykin's reaction kinetics and a nonlocal interaction term in prey growth. The kernel of the integral characterizes nonlocal consumption of resources and depends on space and time. Linear stability analysis determines the conditions of the emergence of Turing patterns without and with nonlocal term, while weakly nonlinear analysis allows the derivation of amplitude equations. The bifurcation analysis and numerical simulation carried out in this work reveal the existence of stationary and dynamic patterns appearing due to the loss of stability of the coexistence homogeneous steady-state.https://www.aimspress.com/article/doi/10.3934/mbe.2020262?viewType=HTMLbazykin’s modelnonlocal interactionhopf bifurcationturing instabilityspatial pattern |
| spellingShingle | Swadesh Pal Malay Banerjee Vitaly Volpert Spatio-temporal Bazykin’s model with space-time nonlocality Mathematical Biosciences and Engineering bazykin’s model nonlocal interaction hopf bifurcation turing instability spatial pattern |
| title | Spatio-temporal Bazykin’s model with space-time nonlocality |
| title_full | Spatio-temporal Bazykin’s model with space-time nonlocality |
| title_fullStr | Spatio-temporal Bazykin’s model with space-time nonlocality |
| title_full_unstemmed | Spatio-temporal Bazykin’s model with space-time nonlocality |
| title_short | Spatio-temporal Bazykin’s model with space-time nonlocality |
| title_sort | spatio temporal bazykin s model with space time nonlocality |
| topic | bazykin’s model nonlocal interaction hopf bifurcation turing instability spatial pattern |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2020262?viewType=HTML |
| work_keys_str_mv | AT swadeshpal spatiotemporalbazykinsmodelwithspacetimenonlocality AT malaybanerjee spatiotemporalbazykinsmodelwithspacetimenonlocality AT vitalyvolpert spatiotemporalbazykinsmodelwithspacetimenonlocality |