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Steady states and spatiotemporal dynamics of a diffusive predator-prey system with predator harvesting

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Názov: Steady states and spatiotemporal dynamics of a diffusive predator-prey system with predator harvesting
Autori: Rongjie Yu, Hengguo Yu, Min Zhao
Zdroj: AIMS Mathematics, Vol 9, Iss 9, Pp 24058-24088 (2024)
Informácie o vydavateľovi: American Institute of Mathematical Sciences (AIMS), 2024.
Rok vydania: 2024
Predmety: non-constant steady states, 0103 physical sciences, QA1-939, turing instability, harvesting, hopf bifurcation, 01 natural sciences, Mathematics
Popis: From the perspective of ecological control, harvesting behavior plays a crucial role in the ecosystem natural cycle. This paper proposes a diffusive predator-prey system with predator harvesting to explore the impact of harvesting on predatory ecological relationships. First, the existence and boundedness of system solutions were investigated and the non-existence and existence of non-constant steady states were obtained. Second, the conditions for Turing instability were given to further investigate the Turing patterns. Based on these conditions, the amplitude equations at the threshold of instability were established using weakly nonlinear analysis. Finally, the existence, direction, and stability of Hopf bifurcation were proven. Furthermore, numerical simulations were used to confirm the correctness of the theoretical analysis and show that harvesting has a strong influence on the dynamical behaviors of the predator-prey systems. In summary, the results of this study contribute to promoting the research and development of predatory ecosystems.
Druh dokumentu: Article
ISSN: 2473-6988
DOI: 10.3934/math.20241170
Prístupová URL adresa: https://doaj.org/article/cbcd3258b6234e07acf5666b0e07b194
Prístupové číslo: edsair.doi.dedup.....3a480ae9e03d76cf8b2510b99b85b129
Databáza: OpenAIRE
Popis
Abstrakt:From the perspective of ecological control, harvesting behavior plays a crucial role in the ecosystem natural cycle. This paper proposes a diffusive predator-prey system with predator harvesting to explore the impact of harvesting on predatory ecological relationships. First, the existence and boundedness of system solutions were investigated and the non-existence and existence of non-constant steady states were obtained. Second, the conditions for Turing instability were given to further investigate the Turing patterns. Based on these conditions, the amplitude equations at the threshold of instability were established using weakly nonlinear analysis. Finally, the existence, direction, and stability of Hopf bifurcation were proven. Furthermore, numerical simulations were used to confirm the correctness of the theoretical analysis and show that harvesting has a strong influence on the dynamical behaviors of the predator-prey systems. In summary, the results of this study contribute to promoting the research and development of predatory ecosystems.
ISSN:24736988
DOI:10.3934/math.20241170