Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect
In this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of se...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2023-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2023/8942147 |
| _version_ | 1797424755018563584 |
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| author | Hang Zhang Yujuan Jiao Jinmiao Yang |
| author_facet | Hang Zhang Yujuan Jiao Jinmiao Yang |
| author_sort | Hang Zhang |
| collection | DOAJ |
| description | In this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results. |
| first_indexed | 2024-03-09T08:06:20Z |
| format | Article |
| id | doaj.art-476e44719820401580037efd7eaabdb8 |
| institution | Directory Open Access Journal |
| issn | 1687-9139 |
| language | English |
| last_indexed | 2024-03-09T08:06:20Z |
| publishDate | 2023-01-01 |
| publisher | Hindawi Limited |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj.art-476e44719820401580037efd7eaabdb82023-12-03T00:00:02ZengHindawi LimitedAdvances in Mathematical Physics1687-91392023-01-01202310.1155/2023/8942147Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching EffectHang Zhang0Yujuan Jiao1Jinmiao Yang2College of Mathematics and Computer ScienceCollege of Mathematics and Computer ScienceCollege of Mathematics and Computer ScienceIn this paper, we are concerned with traveling wave solutions for two preys–one predator system with switching effect. First, we discuss that there is no traveling wave solution for this system by using linearization method. Second, applying super-sub solution method we establish the existence of semitraveling wave solutions with the minimal speed explicitly defined. Moreover, using the method of Lyapunov function and LaSalle’s invariance principle, under certain conditions, we obtain that the semitraveling wave solutions connect the only positive equilibrium point at infinity, are actually traveling wave solutions. Finally, the numerical experiments support the validity of our theoretical results.http://dx.doi.org/10.1155/2023/8942147 |
| spellingShingle | Hang Zhang Yujuan Jiao Jinmiao Yang Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect Advances in Mathematical Physics |
| title | Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect |
| title_full | Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect |
| title_fullStr | Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect |
| title_full_unstemmed | Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect |
| title_short | Existence and Nonexistence of Traveling Wave Solutions for a Reaction–Diffusion Preys–Predator System with Switching Effect |
| title_sort | existence and nonexistence of traveling wave solutions for a reaction diffusion preys predator system with switching effect |
| url | http://dx.doi.org/10.1155/2023/8942147 |
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