Deterministic and stochastic analysis of a prey-dependent predator-prey system

International Journal of Mathematical Education in Science and Technology

Volumn 36, Issue 1, 2005, Pages 65-83

  Maiti, Alakes ^a   Samanta, G P ^b  

^a TAKI GOVERNMENT COLLEGE   (India)

^b INDIAN INSTITUTE OF ENGINEERING SCIENCE AND TECHNOLOGY   (India)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 27844492399     PISSN: 0020739X     EISSN: None     Source Type: Journal    
DOI: 10.1080/00207390412331314980     Document Type: Article

References (27)

1. Ruan, S., and Xiao, D., 2001, SIAM J. Appl. Math., 61, 1445.
2. Holling, C.S., 1965, The functional response of predators to prey density and its role in mimicry and population regulation. Mem. Entomolog. Soc. Can., 45, 3-60.
3. Renshaw, E., 1995, Modelling Biological Population in Space and Time (Cambridge: Cambridge University Press).
4. Dimentberg, M.F., 1988, Statistical Dynamics of Non-linear and Time-varying Systems (New York: John Wiley and Sons).
5. Horsthemke, W., and Lefever, R., 1984, Noise Induced Transitions (Berlin: Springer-Verlag).
6. Samanta, G.P., 1996, Ecol. Model., 91, 283.
7. Samanta, G.P., and Maiti, A., 2003, Syst. Anal. Mod. Simul., 43, 683.
8. Pugachev, V.S., 1963, Theory of Random Function with Application (Oxford: Pergamon Press).
9. Bandyopadhyay, M., and Chakrabarti, C.G., 2003, Deterministic and stochastic analysis of a nonlinear prey-predator system. J. Biol. Sys., 11(2), 161-172.
10. Murray, J.D., 1993, Mathematical Biology (New York: Springer-Verlag).
11. Birkhoff, G., and Rota, G.C., 1982, Ordinary Differential Equations (Boston, MA: Ginn).
12. Freedman, H.I., and Mathsen, R.M., 1993, Bull. Math. Biol., 55, 817.
13. Gard, T.C., 1987, Math. Biosci., 85, 93.
14. Cheng, K.S., Hsu, S.B., and Lin, S.S., 1981, J. Math. Biol., 12, 115.
15. Hale, J.K., 1969, Ordinary Differential Equations (New York: Wiley-Interscience).
16. Hssard, B.D., Kazarinoff, N.D., and Wan, Y.H., 1981, Theory and Application of Hopf-bifurcation (Cambridge: Cambridge University Press).
17. Svirezhev, Yu, M., and Logofet, D.O., 1978, Stability of Biological Communities (Moscow: Mir Publishers).
18. Uhlenbeck, G.E., and Ornstein, L.S., 1954, In: N. Wax (Ed.), Selected Papers on Noise and Stochastic Process (New York: Dover).
19. Wentzel, E., and Ovacharov, L., 1986, Applied Problems on Probability Theory (Moscow: Mir Publishers).
20. Gradshtyen, I.S., and Ryzhik, I.M., 1980, Table of Integrals: Series and Products (New York: Academic Press).
21. Samanta, G.P., and Chakrabatri, C.G., 1991, J. Math. Phys. Sci., 25, 351.
22. May, R.M., 1974, Stability and Complexity in Model Ecosystems (Princeton, NJ: Princeton University Press).
23. Nicolis, G., and Prigogine, I., 1977, Self-organisation in Non-equilibrium Systems (New York: Wiley Interscience).
24. Gardiner, C.G., 1983, Handbook of Stochastic Methods (Berlin: Springer-Verlag).
25. Baishya, M.C., and Chakrabarti, C.G., 1987, Bull. Math. Biol., 49, 125.
26. Samanta, G.P., 1990, Pure Appl. Math. Sci., XXXII, 89.
27. Banerjee, S., and Chakrabarti, C.G., 1998, Syst. Anal. Mod. Simul., 30, 1.