Deterministic property changes in population models under random error perturbations

Ecological Modelling

Volumn 119, Issue 2-3, 1999, Pages 239-247

  Sun, P ^a   Yang, X B ^b  

^a CHINA AGRICULTURAL UNIVERSITY   (China)

^b IOWA STATE UNIVERSITY   (United States)

Author keywords

Chaos; Perturbation; Population model; Random error

Indexed keywords

PERTURBATION; POPULATION MODELING;

EID: 0033565390     PISSN: 03043800     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0304-3800(99)00052-6     Document Type: Article

References (22)

1. Allen, J.C., 1989. Are natural enemy populations chaotic? In: MacDonald, L., Manly, B., Lockwood J., Logan, J. (Eds.), Estimation and Analysis of Insect Populations, Springer-Verlag, Berlin, pp. 190-205.
2. Berryman A.A., Millstein J.A. Are ecological systems chaotic - and if not, why not? Trends Ecol. Evol. 4:1989;26-28.
3. Braiman Y., Lindner J.F., Ditto W.L. Timing spatiotemporal chaos with disorder. Nature. 378:1995;465-467.
4. Costantino R.F., Desharmais R.A., Cushing J.M., Dennis B. Chaotic dynamics in an insect population. Science. 275:1997;389-391.
5. Crutchfield J.P., Farmer J.D., Huberman B.A. Fluctuations and simple chaotic dynamics. Phys. Rep. 92:1982;45-82.
6. Ellner S., Turchin P. Chaos in noisy world: new methods and evidence from time-series analysis. Am. Nat. 145:1995;343-375.
7. Godfray H.C.J., Grenfell B.T. The continuing quest for chaos. Trends Ecol. Evol. 8:1993;43-44.
8. Hassell M.P., Varley G.C. New inductive population model for insect parasites and its bearing on biological control. Nature. 223:1969;1131-1136.
9. Hénon M.A. Two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50:1976;69-78.
10. Kaitala V., Ylikarjula J., Ranta E., Lundberg P. Population dynamics and the colour of environmental noise. Proc. R. Soc. Lond. B. 264:1997;943-948.
11. Lauwerier, H.A., 1986. Two-dimensional iterative maps. In: Holden, A.V. (Ed.), Chaos, Manchester University Press, London, pp. 58-95.
12. Leonard K.J. Stability of equilibria in a gene-for-gene coevolution model of host parasite interactions. Phytopathology. 84:1994;70-77.
13. May R.M. Simple mathematical models with very complex dynamics. Nature. 261:1976;459-467.
14. May R.M., Oster G. Bifurcations and dynamic complexity in simple ecological models. Am. Nat. 110:1976;573-599.
15. Perry J.N., Woiwod I.P., Smith R.H., Morse D. Estimating chaos in an insect population. Science. 276:1997;1881-1882.
16. Pimm S.L. The complexity and stability of ecosystems. Nature. 307:1984;321-326.
17. Rohani P., Miramontes O. Immigration and the persistence of chaos in population models. J. Theor. Biol. 175:1995;203-306.
18. Rohani P., Miramontes O., Hassell M.P. Quasiperiodicity and chaos in population models. Proc. R. Soc. Lond. B. 258:1994;17-22.
19. Schaffer W.M., Ellner S., Kot M. Effects of noise on some dynamical models in ecology. J. Math. Biol. 24:1986;479-523.
20. Stone L. Coloured noise or low-dimensional chaos? Proc. R. Soc. Lond. B. 70(250):1992;81.
21. Stone L. Period-doubling reversals and chaos in simple ecological models. Nature. 365:1993;617-620.
22. Tilman D., Wedin D. Oscillations and chaos in the dynamics of a perennial grass. Nature. 353:1991;653-655.