Positive steady states for a prey-predator model with some nonlinear diffusion terms

By T. Kadota, Kousuke Kuto. 2006

53 citations recorded by the source corpus.

Abstract This paper discusses a prey–predator system with strongly coupled nonlinear diffusion terms. We give a sufficient condition for the existence of positive steady state solutions. Our proof is based on the bifurcation theory. Some a priori estimates for steady state solutions will play an important role in the proof.

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/9607ca21a0af684302f94e60022e51c83b7fbc5b

Citations in the corpus

• Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, unknown): “A realistic form of cross diffusion model for a predator-prey that has appeared in the literature [56] is  ∂u1 ∂t = ∇(2){(α1 + β12 1 + u2 )u1}+ f1u1, ∂u2 ∂t = ∇(2){(α2 + β21u1)u2}+ f2u2.”