Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting
This paper investigates the complex dynamics of a ratio-dependent predator–prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability...
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MDPI AG
2023-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/1/18 |
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| author | Meiyao Chen Yingting Xu Jiantao Zhao Xin Wei |
| author_facet | Meiyao Chen Yingting Xu Jiantao Zhao Xin Wei |
| author_sort | Meiyao Chen |
| collection | DOAJ |
| description | This paper investigates the complex dynamics of a ratio-dependent predator–prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing–Hopf bifurcation; (c) The derivation of the normal form near the Turing–Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results. |
| first_indexed | 2024-03-08T10:57:32Z |
| format | Article |
| id | doaj.art-b58e3c1a92844ee8a44086d774ba8b10 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-08T10:57:32Z |
| publishDate | 2023-12-01 |
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| series | Entropy |
| spelling | doaj.art-b58e3c1a92844ee8a44086d774ba8b102024-01-26T16:22:54ZengMDPI AGEntropy1099-43002023-12-012611810.3390/e26010018Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator HarvestingMeiyao Chen0Yingting Xu1Jiantao Zhao2Xin Wei3Ecological Restoration and Resource Utilization for Cold Region, School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaEcological Restoration and Resource Utilization for Cold Region, School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaEcological Restoration and Resource Utilization for Cold Region, School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaEcological Restoration and Resource Utilization for Cold Region, School of Mathematical Science, Heilongjiang University, Harbin 150080, ChinaThis paper investigates the complex dynamics of a ratio-dependent predator–prey model incorporating the Allee effect in prey and predator harvesting. To explore the joint effect of the harvesting effort and diffusion on the dynamics of the system, we perform the following analyses: (a) The stability of non-negative constant steady states; (b) The sufficient conditions for the occurrence of a Hopf bifurcation, Turing bifurcation, and Turing–Hopf bifurcation; (c) The derivation of the normal form near the Turing–Hopf singularity. Moreover, we provide numerical simulations to illustrate the theoretical results. The results demonstrate that the small change in harvesting effort and the ratio of the diffusion coefficients will destabilize the constant steady states and lead to the complex spatiotemporal behaviors, including homogeneous and inhomogeneous periodic solutions and nonconstant steady states. Moreover, the numerical simulations coincide with our theoretical results.https://www.mdpi.com/1099-4300/26/1/18Turing–Hopf bifurcationstabilitydiffusionpredator–prey modelharvesting rate |
| spellingShingle | Meiyao Chen Yingting Xu Jiantao Zhao Xin Wei Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting Entropy Turing–Hopf bifurcation stability diffusion predator–prey model harvesting rate |
| title | Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting |
| title_full | Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting |
| title_fullStr | Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting |
| title_full_unstemmed | Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting |
| title_short | Turing–Hopf Bifurcation Analysis in a Diffusive Ratio-Dependent Predator–Prey Model with Allee Effect and Predator Harvesting |
| title_sort | turing hopf bifurcation analysis in a diffusive ratio dependent predator prey model with allee effect and predator harvesting |
| topic | Turing–Hopf bifurcation stability diffusion predator–prey model harvesting rate |
| url | https://www.mdpi.com/1099-4300/26/1/18 |
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