References
- H. Amann, Dynamic theory of quasilinear parabolic equations, III. Global Existence, Math Z. 202 (1989), 219-250
- H. Amann, Dynamic theory of quasilinear parabolic equations, II. Reaction-diffusion systems, Differential and Integral Equations 3 (1990), no. 1, 13-75
- H. Amann, Non-homogeneous linear and quasilinear elliptic and parabolic boundary value problems, Function spaces, differential operators and nonlinear analysis (Friedrichroda, 1992), 9-126, Teubner-Texte Math., 133, Teubner, Stuttgart, 1993
- H. Freedman, Deterministic Mathematical Models in Population Ecology, Marcel Dekker, New York, 1980
- A. Friedman, Partial Differential Equations, Holt, Rinehart and Winston, New York, 1969
- C. Holling, The functional response of predators to prey density and its role in mimicry and population regulation, Mem. Ent. Soc. Can. 45 (1965), 1-65
- W. Ko and I. Ahn, Positive coexistence for a simple food chain model with ratiodependent functional response and cross-diffusion, Commun. Korean Math. Soc. 21 (2006), no. 4, 701-717 https://doi.org/10.4134/CKMS.2006.21.4.701
- Y. Kuang and H. Freedman, Uniqueness of limit cycles in Gause-type models of predator-prey system, Math. Biosci. 88 (1988), 67-84 https://doi.org/10.1016/0025-5564(88)90049-1
- K. Kuto and Y. Yamada, Multiple coexistence states for a prey-predator system with cross-diffusion, J. Differential Equations 197 (2004), no. 2, 315-348 https://doi.org/10.1016/j.jde.2003.08.003
- R. May, Stability and Complexity in Model Ecosystems, 2nd ed., Princeton Univ. press, Princeton, 1974
- L. Nirenberg, On elliptic partial differential equations, Ann. Scuo. Norm. Sup. Pisa 13(3) (1959), 115-162
- A. Okubo and L. A. Levin, Diffusion and Ecological Problems : modern perspective, Interdisciplinary Applied Mathematics, 2nd ed., Vol. 14, Springer, New York, 2001
- C. Pao, Strongly coupled elliptic systems and applications to Lotka-Volterra models with cross-diffusion, Nonlinear Analysis, 60 (2005), 1197-1217 https://doi.org/10.1016/j.na.2004.10.008
- L. Real, Ecological determinants of functioal response, Ecology 60 (1979), 481-485 https://doi.org/10.2307/1936067
- K. Ryu and I. Ahn, Coexistence theorem of steady states for nonlinear self-cross diffusion system with competitive dynamics, J. Math. Anal. Appl. 283 (2003), 46-65 https://doi.org/10.1016/S0022-247X(03)00162-8
- K. Ryu and I. Ahn, Positive steady-states for two interacting species models with linear self-cross diffusions, Discrete Contin. Dynam. Systems 9 (2003), 1049-1061 https://doi.org/10.3934/dcds.2003.9.1049
- S.-A. Shim, Long-time properties of prey-predator system with cross-diffusion, Commun. Korean Math. Soc. 21 (2006), no. 2, 293-320 https://doi.org/10.4134/CKMS.2006.21.2.293
- S.-A. Shim, On the properties of solutions to predator-prey models with cross-diffusions, Proceedings of the National institute for Mathematical Sciences Vol. 1 (2006), no. 2, 100-110
- M. A. Tsyganov, J. Brindley, A. V. Holden, and V. N. Biktashev, Soliton-like phenomena in one-dimensional cross-diffusion systems: a predator-prey pursuit and evasion example, Phys. D 197 (2004), no. 1-2, 18-33 https://doi.org/10.1016/j.physd.2004.06.004
- X. Zeng, Non-constant positive steady states of a prey-predator system with crossdiffusions, J. Math. Anal. Appl. 332 (2007), no. 2, 989-1009 https://doi.org/10.1016/j.jmaa.2006.10.075
Cited by
- On stability of two degenerate reaction–diffusion systems vol.390, pp.1, 2012, https://doi.org/10.1016/j.jmaa.2012.01.032
- EXISTENCE OF GLOBAL SOLUTIONS FOR A PREY–PREDATOR MODEL WITH CROSS-DIFFUSION vol.03, pp.02, 2010, https://doi.org/10.1142/S1793524510000908