Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect
In this paper we studied traveling front solutions of a single species model with cannibalism and nonlocal effect. For a particular class of kernels, the existence of traveling front solutions connecting the extinction state with the positive equilibrium was established for the strongly nonlocal eff...
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AIMS Press
2024-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.20241298?viewType=HTML |
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| _version_ | 1850263940511039488 |
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| author | Xijun Deng Aiyong Chen |
| author_facet | Xijun Deng Aiyong Chen |
| author_sort | Xijun Deng |
| collection | DOAJ |
| description | In this paper we studied traveling front solutions of a single species model with cannibalism and nonlocal effect. For a particular class of kernels, the existence of traveling front solutions connecting the extinction state with the positive equilibrium was established for the strongly nonlocal effect case. Our approach was to reformulate it as a singular perturbed problem, and then tackle this problem by using dynamical systems techniques, in particular, geometric singular perturbation theory and Fenichel's invariant manifold theory. |
| format | Article |
| id | doaj-art-7f0afcaca34b4de59ee5799479e43883 |
| institution | OA Journals |
| issn | 2473-6988 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj-art-7f0afcaca34b4de59ee5799479e438832025-08-20T01:54:50ZengAIMS PressAIMS Mathematics2473-69882024-09-01910266882670110.3934/math.20241298Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effectXijun Deng0Aiyong Chen11. School of Mathematics, Physics and Optoelectronic Engineering, Hubei University of Automotive Technology, Shiyan, 442002, China 2. Department of Mathematics and Physics, Hunan University of Arts and Science, Changde, 415000, China3. Department of Mathematics, Hunan First Normal University, Changsha, 410205, ChinaIn this paper we studied traveling front solutions of a single species model with cannibalism and nonlocal effect. For a particular class of kernels, the existence of traveling front solutions connecting the extinction state with the positive equilibrium was established for the strongly nonlocal effect case. Our approach was to reformulate it as a singular perturbed problem, and then tackle this problem by using dynamical systems techniques, in particular, geometric singular perturbation theory and Fenichel's invariant manifold theory.https://aimspress.com/article/doi/10.3934/math.20241298?viewType=HTMLtraveling wave frontstrongly nonlocal effectcannibalismgeometric singular perturbation theoryinvariant manifold theory |
| spellingShingle | Xijun Deng Aiyong Chen Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect AIMS Mathematics traveling wave front strongly nonlocal effect cannibalism geometric singular perturbation theory invariant manifold theory |
| title | Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| title_full | Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| title_fullStr | Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| title_full_unstemmed | Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| title_short | Traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| title_sort | traveling wave fronts in a single species model with cannibalism and strongly nonlocal effect |
| topic | traveling wave front strongly nonlocal effect cannibalism geometric singular perturbation theory invariant manifold theory |
| url | https://aimspress.com/article/doi/10.3934/math.20241298?viewType=HTML |
| work_keys_str_mv | AT xijundeng travelingwavefrontsinasinglespeciesmodelwithcannibalismandstronglynonlocaleffect AT aiyongchen travelingwavefrontsinasinglespeciesmodelwithcannibalismandstronglynonlocaleffect |