Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
Abstract: In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf bifurcation and the stability of the bifurcating periodic solution by the center manifold and the normal form theory. For the reaction-diffusion model, first it is shown that Turing instability occurs, then the direction and stability of the Hopf bifurcation is reached. Our results show that hunting cooperation plays a crucial role in the dynamics of the model, that is, it can be beneficial to the predator population and induce the rise of Turing instability. Finally, numerical simulations are performed to visualize the complex dynamic behavior.
- Location
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Deutsche Nationalbibliothek Frankfurt am Main
- Extent
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Online-Ressource
- Language
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Englisch
- Bibliographic citation
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Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation ; volume:20 ; number:1 ; year:2022 ; pages:986-997 ; extent:12
Open mathematics ; 20, Heft 1 (2022), 986-997 (gesamt 12)
- Creator
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Miao, Liangying
He, Zhiqian
- DOI
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10.1515/math-2022-0474
- URN
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urn:nbn:de:101:1-2022091314074350513355
- Rights
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Last update
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15.08.2025, 7:32 AM CEST
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Associated
- Miao, Liangying
- He, Zhiqian
Other Objects (12)
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Bifurcation analysis in a diffusive predator–prey system with Michaelis–Menten-type predator harvesting
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Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting
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Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model
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Bogdanov–Takens bifurcation in a predator–prey model
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Diffusive induced global dynamics and bifurcation in a predator-prey system
Turing–Hopf bifurcation of a ratio-dependent predator-prey model with diffusion
Persistence and Turing instability in a cross-diffusive predator–prey system with generalist predator
Hopf bifurcation of a delayed diffusive predator-prey model with strong Allee effect
Bifurcation analysis in a diffusive predator–prey system with Michaelis–Menten-type predator harvesting
Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity
Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting
Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior
Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model
Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
Bogdanov–Takens bifurcation in a predator–prey model
Stability and Hopf bifurcation of a predator-prey model
Diffusive induced global dynamics and bifurcation in a predator-prey system
Turing–Hopf bifurcation of a ratio-dependent predator-prey model with diffusion
Persistence and Turing instability in a cross-diffusive predator–prey system with generalist predator
Hopf bifurcation of a delayed diffusive predator-prey model with strong Allee effect
Bifurcation analysis in a diffusive predator–prey system with Michaelis–Menten-type predator harvesting
Time delay induced Hopf bifurcation in a diffusive predator–prey model with prey toxicity
Turing instability and Hopf bifurcation in a predator–prey model with delay and predator harvesting
Hopf bifurcation in a diffusive predator–prey model with Smith growth rate and herd behavior
Density-dependent effects on Turing patterns and steady state bifurcation in a Beddington–DeAngelis-type predator–prey model
Delay-induced Hopf bifurcation in a diffusive Holling–Tanner predator–prey model with ratio-dependent response and Smith growth
Bogdanov–Takens bifurcation in a predator–prey model