Global existence and convergence to steady states for a predator-prey model with both predator- and prey-taxis

DOI10.3934/dcds.2021136zbMath1482.35043OpenAlexW3200218667WikidataQ113201481 ScholiaQ113201481MaRDI QIDQ2070882

Guoqiang Ren, Bin Liu

Publication date: 24 January 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2021136

zbMATH Keywords

predator-preyprey-taxisasymptotically stable steady state, triple cross diffusionpredator-taxis

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Reaction-diffusion equations (35K57) Population dynamics (general) (92D25) Cell movement (chemotaxis, etc.) (92C17) Initial-boundary value problems for second-order parabolic systems (35K51)

Related Items

Existence Theory and Qualitative Analysis for a Fully Cross-Diffusive Predator-Prey System, Global solutions near homogeneous steady states in a fully cross-diffusive predator-prey system with density-dependent motion, Complex dynamics of a predator–prey model with opportunistic predator and weak Allee effect in prey, On a quasilinear fully parabolic predator-prey model with indirect pursuit-evasion interaction, Existence and qualitative analysis of a fully cross-diffusive predator-prey system with nonlinear taxis sensitivity, Global bifurcation of coexistence states for a prey-predator model with prey-taxis/predator-taxis, Global boundedness of a three-species predator-prey model with prey-taxis and competition, Global generalized solutions to a three species predator-prey model with prey-taxis

Cites Work

• Unnamed Item
• Global boundedness of solutions in a reaction-diffusion system of predator-prey model with prey-taxis
• Boundedness and global stability of the two-predator and one-prey models with nonlinear prey-taxis
• Global stability of prey-taxis systems
• A fully cross-diffusive two-component evolution system: existence and qualitative analysis via entropy-consistent thin-film-type approximation
• Initiation of slime mold aggregation viewed as an instability
• Persistence and global stability of positive periodic solutions of three species food chains with omnivory
• Global existence of classical solutions to a predator-prey model with nonlinear prey-taxis
• A reaction-diffusion system modeling predator-prey with prey-taxis
• The Volterra model for three species predator-prey systems: Boundedness and stability
• Global dynamics for a diffusive predator-prey model with prey-taxis and classical Lotka-Volterra kinetics
• Global existence and asymptotic behavior in a two-species chemotaxis system with logistic source
• Asymptotic behavior analysis for a three-species food chain stochastic model with regime switching
• Global solution for a general cross-diffusion two-competitive-predator and one-prey system with predator-taxis
• Global existence of solutions and uniform persistence of a diffusive predator-prey model with prey-taxis
• Global Solutions near Homogeneous Steady States in a Multidimensional Population Model with Both Predator- and Prey-Taxis
• Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics
• Toward a mathematical theory of Keller–Segel models of pattern formation in biological tissues