The dynamics of a predator-prey model with diffusion and indirect prey-taxis

DOI10.1007/S10884-019-09778-7zbMath1445.35075OpenAlexW2956941440WikidataQ115603921 ScholiaQ115603921MaRDI QIDQ785376

Mingxin Wang, Jian-ping Wang

Publication date: 6 August 2020

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10884-019-09778-7

zbMATH Keywords

diffusive predator-prey modelglobal existence and boundednessglobal stability and convergence rateindirect prey-taxis

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Initial-boundary value problems for second-order parabolic systems (35K51)

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Cites Work

• Unnamed Item
• Unnamed Item
• Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis
• Nonconstant positive steady states and pattern formation of 1D prey-taxis systems
• Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis
• Global stability of prey-taxis systems
• Dynamic theory of quasilinear parabolic equations. II: Reaction-diffusion systems
• A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment
• Continuous traveling waves for prey-taxis
• Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis
• Aggregation vs. global diffusive behavior in the higher-dimensional Keller-Segel model
• A reaction-diffusion system modeling predator-prey with prey-taxis
• Geometric theory of semilinear parabolic equations
• Advection-diffusion equations for generalized tactic searching behaviors
• Note on the Lyapunov functional method
• Dynamics for a diffusive prey-predator model with different free boundaries
• The diffusive logistic equation with a free boundary and sign-changing coefficient
• Boundedness vs. blow-up in a chemotaxis system
• Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
• Predator–prey model with diffusion and indirect prey-taxis
• The diffusive Beddington‐DeAngelis predator‐prey model with nonlinear prey‐taxis and free boundary
• Global bifurcation of solutions for a predator–prey model with prey‐taxis
• Pattern formation in prey-taxis systems
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues

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