Turing and hopf patterns formation in a predator-prey model with leslie-gower-type functional response

Dynamics of Continuous, Discrete and Impulsive Systems Series B: Applications and Algorithms

Volumn 16, Issue 4, 2009, Pages 479-488

  Camara, Baba Issa ^a   Aziz Alaoui, M A ^a  

^a UNIVERSITÉ DU HAVRE   (France)

Author keywords

Bifurcations; Hopf; Predator prey; Reaction diffusion; Turing

Indexed keywords

EID: 70449709814     PISSN: 14928760     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (21)

1. M. A. Aziz-Alaoui, Study of a Leslie-Gower-type tritrophic population model, Chaos, Solitons and Fractals, 14 (8), (2002), 1275-1293.
2. M.A. Aziz-Alaoui and M. Daher Okiye, Boundedness and global stability for a predator-prey model with modified Leslie-Gower and Holling type II shemes, Applied Math. Let., 16, (2003), 1069-1075.
3. B.I. Camara and M.A. Aziz-Alaoui, Dynamics of predator-prey model with diffusion, Dynamics of Continuous, Discrete and Impulsive System, series A , 15, (2008) 897-906
4. R.S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: population models in disrupted environnementts, Proc. Ro. Soc., (1989) 293-318.
5. O. M. Daher and M.A. Aziz-Alaoui, On the dynamics of a predator-prey model with the Holling-Tanner functional response, MIRIAM Editions, Editor V. Capasso, Proc. ESMTB conf., (2002) 270-278.
6. J.K. Hale and P. Waltman, Persistence in infinite-dimensionnal systems, SIAM J. Math. Ana., 20(2), (1989) 388-395.
7. P. Hess, Periodic-parabolic boundary value problems and positivity, Pitman research notes in Mathematics series, 247 (1991).
8. C. Letellier and M.A. Aziz-Alaoui, Analysis of the dynamics of a realistic ecological model, Chaos, Solitons and Fractals, 13 (1), (2002) 95-107.
9. C. Letellier, L. Aguirre, J. Maquet and M.A. Aziz-Alaoui, Should all the species of a food chain be counted to investigate the global dynamics, Chaos, Solitons and Fractals, 13 (1), (2002) 1099-1113.
10. Z. Lin and M. Pedersen, Stability in a diffusive food-chain model with Michaelis-Menten functional responses, Nonlinear Anal., 57, (2004) 421-433.
11. R.T. Liu, S.S. Liaw and P.K. Maini, Oscillatory Turing Patterns in a Simple Reaction Diffusion System, Journal of the Korean Physical Soc., 50(1), (2007) 234-238.
12. A. Morozov, S. Petrovskii and B.L. Li, Bifurcations and chaos in a prey datorprey system with the Allee effect, The Royal Society Lond., 271, (2004) 1407-1414.
13. J. D. Murray, Mathematical biology, Springer-Verlag Berlin Heidelberg (1993).
14. J. D. Murray, Mathematical biology : II. Spatial Models and Biomedical Applications, Springer-Verlag Berlin Heidelberg (2003).
15. J. D. Murray, On pattern-formation mechanisms for lepidopteran wing patterns and mammalian coat markings, Philos. Trans. R. Soc. Lond., Ser. B Biol. Sci., 295, (1981) 473-496.
16. A.F. Nindjin, M.A. Aziz-Alaoui and M. Cadivel, Analysis of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes with Time Delay, Nonlinear Anal. Real World Appl., 7(5), (2006) 1104-1118.
17. A.F. Nindjin and M.A. Aziz-Alaoui, Persistence and global stability in a delayed Leslie-Gower type three species food chain, J. Math. Ana. Ap., 340(1), (2008) 340-357.
18. X. Song and Y. Li, Dynamics behaviors of the periodic predator-prey model with modified Leslie-Gower Holling-type II schemes and impulsive effect, Nonlinear Anal. Real World Appl., 9(1), (2008) 64-79.
19. A. Turing, The chemical basis of morphogenesis, Phil. Trans. R. Soc. London B 237, (1952) 37-72.
20. [20] L. Yang, M. Dolnik, A.M. Zhabotinsky and I.R. Epstein, Pattern formation, arising from interactions between Turing and wave instabilities, J. Chem. Phys., 117(15), (2002) 7259-7265. (Pubitemid 35354171)
21. L. Zhang, W. Wang and Y. Xue, Spatiotemporal complexity of a predator-prey system with constant harvest rate. Chaos, Solitons and Fractals, to appear (2009).