论文信息 - Coexistence problem for a prey–predator model with density-dependent diffusion

Coexistence problem for a prey–predator model with density-dependent diffusion

Abstract We study a prey–predator model with nonlinear diffusions. In a case when the spatial dimension is less than 5, a universal bound for coexistence steady-states is found. By using the bound and the bifurcation theory, we obtain the bounded continuum of coexistence steady-states.

Yoshio Yamada | Kousuke Kuto | Kousuke Kuto | Yoshio Yamada

[1] Masayasu Mimura,et al. Diffusion, Cross-diffusion and Competitive Interaction , 2006, Journal of mathematical biology.

[2] Yoshio Yamada. Chapter 6 - Positive Solutions for Lotka–Volterra Systems with Cross-Diffusion , 2008 .

[3] Phan Văn Tuộc. Global existence of solutions to Shigesada-Kawasaki-Teramoto cross-diffusion systems on domains of arbitrary dimensions , 2007 .

[4] Paul H. Rabinowitz,et al. Some global results for nonlinear eigenvalue problems , 1971 .

[5] Yuan Lou,et al. DIFFUSION VS CROSS-DIFFUSION : AN ELLIPTIC APPROACH , 1999 .

[6] D. Gilbarg,et al. Elliptic Partial Differential Equa-tions of Second Order , 1977 .

[7] Kousuke Kuto,et al. Positive steady states for a prey-predator model with some nonlinear diffusion terms , 2006 .

[8] Edward Norman Dancer,et al. Bifurcation from Simple Eigenvalues and Eigenvalues of Geometric Multiplicity One , 2002 .

[9] Wonlyul Ko,et al. On a predator–prey system with cross diffusion representing the tendency of predators in the presence of prey species , 2008 .

[10] M. Crandall,et al. Bifurcation from simple eigenvalues , 1971 .

[11] N. Shigesada,et al. Spatial segregation of interacting species. , 1979, Journal of theoretical biology.