A unifying framework for chaos and stochastic stability in discrete population models

Journal of Mathematical Biology

Volumn 35, Issue 5, 1997, Pages 557-588

  Vellekoop, M H ^a   Hognas G ^b  

^a IMPERIAL COLLEGE LONDON   (United Kingdom)

^b ÅBO AKADEMI UNIVERSITY   (Finland)

Author keywords

Chaos; Invariant measures; Markov processes; Population dynamics; Recurrence

Indexed keywords

EID: 0001112177     PISSN: 03036812     EISSN: None     Source Type: Journal    
DOI: 10.1007/s002850050066     Document Type: Article

References (18)

1. Devaney, R. L.: An Introduction to Chaotic Dynamical Systems (2nd edition). New York: Addison-Wesley 1989
2. Gyllenberg, M., Högnäs, G. and Koski, T.: Population Models with Environmental Stochasticity. Journal of Mathematical Biology 32, 93-108 (1994)
3. Gyllenberg, M., Högnäs, G. and Koski, T.: Null Recurrence in a Stochastic Ricker Model. In: M. Gyllenberg and L. E. Persson (eds): Analysis, Algebra and Computers in Mathematical Research, Proceedings of the Twenty-first Nordic Congress of Mathematicians (pp. 147-164). New York: Marcel Dekker 1994
4. Hassell, M. P.: Density-Dependence in Single-Species Populations. Journal of Animal Ecology 44, 283-296 (1974)
5. Hassell, M. P., Lawton, J. H. and May, R. M.: Patterns of Dynamical Behaviour in Single Species Population Models. Journal of Animal Ecology 45, 471-486 (1976)
6. Hastings, A., Hom, C. L., Turchin, P. and Godfray, H. C. J.: Chaos in Ecology: Is Mother Nature a Strange Attractor? Annual Review of Ecology and Systematics 24, 1-33 (1993)
7. Karlin, T. and Taylor, H. M.: A First Course in Stochastic Processes (2nd edition). New York: Academic Press 1975
8. Latto, J.: The Analysis of Density Dependence in Insect Populations (PhD thesis, Department of Pure and Applied Biology, Imperial College). London, 1989
9. Li, T.-Y. and Yorke, J. A.: Period Three implies Chaos. American Mathematical Monthly 82, 985-992 (1976)
10. May, R. M.: Simple Mathematical Models with Very Complicated Dynamics. Nature 261, 459-467 (1976)
11. May, R. M. and Oster, G. F.: Bifurcations and Dynamic Complexity in Simple Ecological Models. American Nature 110, 573-599 (1976)
12. Meyn, S. P. and Tweedie, R. L.: Markov Chains and Stochastic Stability (Control and Communication in Engineering Series). New York: Springer-Verlag 1993
13. Morris, W. F.: Problems in Detecting Chaotic Behaviour in Natural Populations by Fitting Simple Discrete Models. Ecology 71, 1849-1862 (1990)
14. Ricker, W. E.: Stock and Recruitment. Journal of the Fisheries Research Board of Canada 11, 559-623 (1954)
15. Tweedie, R. L.: Criteria for Classifying General Markov Chains. Adv. Appl. Prob. 8, 737-771 (1976)
16. Varley, G. C., Gradwell, G. R. and Hassell, M. P.: Insect Population Ecology. Oxford: Blackwell Scientific Publications 1973
17. Vellekoop, M. H.: Analysis of Ecological Systems: Chaos, Stochastics and Optimisation (Internal Report, Department of Applied Mathematics, University of Twente). Enschede, 1993
18. Vellekoop, M. H. and Berglund, R.: On Intervals, Transitivity = Chaos. American Mathematical Monthly 101, 353-355 (1994)