Stochastic analysis of time-delayed ecosystems

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 76, Issue 4, 2007, Pages

  Cai, G Q ^a   Lin, Y K ^a  

^a FLORIDA ATLANTIC UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

PARAMETER ESTIMATION; PROBABILITY DISTRIBUTIONS; RANDOM PROCESSES; SYSTEMS ANALYSIS; TIME DELAY;

PREDATOR POPULATION; STOCHASTIC ANALYSIS; TIME-DELAYED ECOSYSTEMS;

ECOSYSTEMS;

EID: 35448970950     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.76.041913     Document Type: Article

References (26)

1. A. J. Lotka, Elements of Physical Biology (William and Wilkins, Baltimore, NJ, 1925).
2. V. Volterra, Mem. Acad. Lincei 2, 31 (1926).
3. V. Volterra, Lecons sur la theorie mathematique de la lutte pour la vie (Gauthiers-Vilars, Paris, 1931).
4. R. M. May, Stability and Complexity in Model Ecosystems (Oxford University Press, New York, 1973).
5. R. M. May, Theoretical Ecology, Principles and Applications, 2nd ed. (Sinauer Associates, Sunderland, MA, 1981).
6. J. D. Murray, Mathematical Biology (Springer, New York, 1993).
7. M. L. Rosenzweig and R. H. MacArthue, Am. Nat. AMNTA4 0003-0147 97, 205 (1963).
8. A. D. Bazykin, Nonlinear Dynamics of Interacting Populations (World Scientific, Singapore, 1998).
9. G. E. Hutchinson, Ann. N.Y. Acad. Sci. ANYAA9 0077-8923 10.1111/j.1749-6632.1948.tb39854.x 50, 221 (1948).
10. N. MacDonald, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(76)90130-9 28, 321 (1976).
11. N. MacDonald, Math. Biosci. MABIAR 0025-5564 10.1016/0025-5564(77)90140-7 33, 227 (1977).
12. R. Nisbet and W. Gurney, Modeling Fluctuating Populations (Wiley, New York, 1982).
13. E. Korpimaki, Oikos OIKSAA 0030-1299 10.2307/3545265 62, 195 (1993).
14. B. Hornfeldt, Ecology ECOLAR 0012-9658 10.2307/1941735 75, 791 (1994).
15. P. Turchin, Complex Population Dynamics (Princeton University Press, Princeton, 2003).
16. L. Arnold, W. Horthemke, and J. W. Stucki, Biom. J. BIJODN 0323-3847 21, 451 (1979).
17. A. F. Rozenfeld, Phys. Lett. A PYLAAG 0375-9601 10.1016/S0375-9601(01) 00033-0 280, 45 (2001).
18. R. Z. Khasminskii and F. C. Klebaner, Ann. Appl. Probab. ZZZZZZ 1050-5164 11, 952-963 (2001).
19. M. F. Dimentberg, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.65. 036204 65, 036204 (2002).
20. M. F. Dimentberg, in Proceedings of IUTAM Symposium on Nonlinear Stochastic Dynamics, edited by, N. Sri Namachchivaya, and, Y. K. Lin, (Kluwer Academic, Dordrecht, 2003), pp. 307-317.
21. G. Q. Cai and Y. K. Lin, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.70.041910 70, 041910 (2004).
22. R. L. Stratonovich, Topics in the Theory of Random Noise (Gordon and Breach, New York, 1963), Vol. 1.
23. R. Z. Khasminskii, Theor. Probab. Appl. TPRBAU 0040-585X 10.1137/1112019 12, 144 (1966).
24. Y. K. Lin and G. Q. Cai, Probabilistic Structure Dynamics (MacGraw-Hill, New York, 2004).
25. K. Itò, Mem. Am. Math. Soc. MAMCAU 0065-9266 4, 289 (1951).
26. K. Itò, Nagoya Math. J. NGMJA2 0027-7630 3, 55 (1951).