On a predator-prey system with cross diffusion representing the tendency of predators in the presence of prey species

DOI10.1016/j.jmaa.2007.11.018zbMath1160.35021OpenAlexW2059762169WikidataQ115570441 ScholiaQ115570441MaRDI QIDQ2480344

Wonlyul Ko, Kimun Ryu

Publication date: 31 March 2008

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jmaa.2007.11.018

zbMATH Keywords

Lotka-Volterra systempredator-prey interactioncross diffusionupper and lower solution

Mathematics Subject Classification ID

PDEs in connection with biology, chemistry and other natural sciences (35Q92) Population dynamics (general) (92D25)

Related Items

Steady state for a predator-prey cross-diffusion system with the Beddington-DeAngelis and Tanner functional response, Turing pattern formation in a predator-prey system with cross diffusion, A Lotka-Volterra competition model with cross-diffusion, Pattern formation in a cross-diffusive ratio-dependent predator-prey model, Turing patterns of a strongly coupled predator-prey system with diffusion effects, Pattern formation in a cross-diffusive Holling-Tanner model, Coexistence problem for a prey-predator model with density-dependent diffusion, Steady state in a cross-diffusion predator-prey model with the Beddington-DeAngelis functional response, Local dynamics and coexistence of predator-prey model with directional dispersal of predator, Complex patterns in a predator-prey model with self and cross-diffusion, Coexistence states of a ratio-dependent predator-prey model with nonlinear diffusion, Dynamical analysis of a plateau pika with cross-diffusion under contraception control, Spatial patterns of the Holling–Tanner predator–prey model with nonlinear diffusion effects, Bifurcation of Reaction Cross-Diffusion Systems

Cites Work

• Diffusion vs cross-diffusion: An elliptic approach
• Coexistence theorem of steady states for nonlinear self-cross diffusion systems with competitive dynamics.
• Multiple coexistence states for a prey-predator system with cross-diffusion.
• Diffusion and ecological problems: Modern perspectives.
• Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion
• Diffusion, self-diffusion and cross-diffusion
• Coexistence Theorems of Steady States for Predator-Prey Interacting Systems
• Positive solutions of a class of biological models in a heterogeneous environment
• Nonlinear elliptic boundary-value problems in unbounded domains
• Some mathematical models for population dynamics that lead to segregation