Stationary patterns of a predator-prey model with spatial effect

Applied Mathematics and Computation

Volumn 216, Issue 12, 2010, Pages 3620-3626

  Zhu, Li Mei ^a   Wang, Ai Ling ^a   Liu, Yong Jiang ^a   Wang, Biao ^a  

^a NORTH UNIVERSITY OF CHINA   (China)

Author keywords

Cross diffusion; Pattern formation; Predator prey

Indexed keywords

CRITICAL LINES; CROSS-DIFFUSION; MATHEMATICAL THEORY; PREDATOR-PREY; PREDATOR-PREY MODELS; SPATIAL DOMAINS; SPATIAL EFFECT; SPATIAL PATTERNS; STATIONARY PATTERNS; TURING BIFURCATION; TWO PARAMETER;

HOPF BIFURCATION;

DIFFUSION;

EID: 77953611519     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2010.05.007     Document Type: Article

References (15)

1. Tanner J.T. The stability and the intrinsic growth rates of prey and predator populations. Ecology 56 (1975) 855-867
2. Levin S.A., Powell T.M., and Steele J.H. Patch Dynamics Lecture Notes in Biomathematics (1993), Springer-Verlag, Berlin
3. Dubey B., Das B., and Hussain J. A predator-prey interaction model with self and cross-diffusion. Ecol. Model. 141 (2001) 67-76
4. Wollkind D.J., Collings J.B., and Logan J.A. Metastability in a temperature-dependent model system for predator-prey mite outbreak interactions on fruit flies. Bull. Math. Biol. 50 (1988) 379-409
5. Saez E., and Gonzalez-Olivares E. Dynamics of a predator-prey model. SIAM J. Appl. Math. 59 (1999) 1867-1878
6. Hsu S.-B., and Huang T.-W. Global stability for a class of predator-prey systems. SIAM J. Appl. Math. 55 3 (1995) 763-783
7. Ouyang Q. Pattern Formation in a Reaction-Diffusion Systems (2000), Scientific and Technological Education Publishing House, Shanghai (in Chinese)
8. Murray J.D. Mathematical Biology. second ed. (1993), Springer-Verlag, Berlin, New York
9. Chung J.M., and Peacock-López E. Bifurcation diagrams and Turing patterns in a chemical self-replicating reaction-diffusion system with cross diffusion. J. Chem. Phys. 127 (2007) 174903
10. Chung J.M., and Peacock-López E. Cross-diffusion in the templator model of chemical self-replication. Phys. Let. A 371 (2007) 41-47
11. Alonso D., Bartumeus F., and Catalan J. Mutual interference between predators can give rise to Turing spatial patterns. Ecology 83 (2002) 28-34
12. Baurmann M., Gross T., and Feudel U. Instabilities in spatially extended predator-prey systems: spatio-temporal patterns in the neighborhood of Turing-Hopf bifurcations. J. Theor. Biol. 245 (2007) 220-229
13. Cushing J.M., Costantino R.F., Dennis B., Desharnais R.A., and Henson S.M. Chaos in Ecology: Experimental Nonlinear Dynamics (2003), Academic, San Diego
14. Morozov A., Petrovskii S., and Li B.-L. Bifurcations and chaos in a predator-prey system with the allee effect. Proc. R. Soc. Lond. B 271 (2004) 1407-1414
15. Garvie M.R. Finite-difference schemes for reaction-diffusion equations modeling predator-prey interactions in matlab. Bull. Math. Biol. 69 (2007) 931-956