The stochastic Beverton-Holt equation and the M. Neubert conjecture

Journal of Dynamics and Differential Equations

Volumn 17, Issue 4, 2005, Pages 825-844

  Haskell, Cymra ^a   Sacker, Robert J ^a  

^a UNIVERSITY OF SOUTHERN CALIFORNIA   (United States)

Author keywords

Population biology; Skew product dynamical system; Stochastic difference equation

Indexed keywords

EID: 27844540277     PISSN: 10407294     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10884-005-8273-x     Document Type: Article

References (25)

1. Allen, L. J. S. (2003). An Introduction to Stochastic Processes with Applications to Biology, Pearson Prentice Hall, New Jersey.
2. Arnold, L. (1998). Random Dynamical Systems, Springer, New York.
3. Berger, A., and Siegmund, S. (2003). On the gap between random dynamical systems and continuous skew products. J. Dyn. Differential Eqs, 15(2/3), 237-279.
4. Beverton, R. J. H., and Holt, S. J. (1957). On the dynamics of exploited fish populations. Fishery invest. 19, 1-533.
5. Billingsley, P. (1995). Probability and Measure, Wiley, New York, third edition.
6. Borovkov, A. A. (2001). Ergodicity and Stability of Stochastic Processes, Wiley, New York.
7. Caswell, H. H. (2001). Matrix Population Models: Construction, Analysis and Interpretation. Sinauer Assoc., Sunderland, MA, USA, second edition.
8. Chueshov, I. (2002). Monotone Random Systems - Theory and Applications, Lecture Notes in Mathematics, LNM 1779, Springer, Berlin.
9. Clark, C. W. (1990). The Optimal Management of Renewable Resources, John Wiley, New York.
10. Clark, M. E., and Gross, L. J. (1990). Periodic solutions of non-autonomous difference equations. Math. Biosci. 102, 105-119.
11. Cushing, J. M., and Henson, S. M. (2001). Global dynamics of some periodically forced, monotone difference equations. J. Difference Eq. Appl. 7, 859-872.
12. Cushing, J. M., and Henson, S. M. (2002). A periodically forced Beverton-Holt equation. J. Difference Eq. Appl. 8, 1119-1120.
13. Elaydi, S., and Sacker, R. J. (2005). Non-autonomous Beverton-Holt equations and the Cushing-Henson conjectures. J. Difference Eq. Appl. 11(4-5), 337-346.
14. Elaydi, S., and Sacker, R. J. (2004). Global stability of periodic orbits of non-autonomous difference equations. J. Differential Eqs. 208(11), 258-273.
15. Elaydi, S., and Sacker, R. J. (2004). Global stability of periodic orbits of non-autonomous difference equations in population biology and the Cushing-Henson conjecture. Proceedings of the 8th International Conference on Difference Eq. and Applied (ICDEA2003) Chapman and Hall/CRC 2005, 113-126.
16. Franke J., and Seigrade, J. (2003). Attractors for discrete periodic dynamical systems. J. Math. Anal. Appl., 286(1), 64-79.
17. Kifer, Y. (1986). Ergodic Theory of Random Transformations, Birkhäuser, Boston, Basel, Stuttgart.
18. Kocic, V. L. (2005). A note on the Nonautonomous Beverton-Holt Model. J. Difference Eq. Appl. 11(4-5), 415-422.
19. Kon, R. (2004). A note on attenuant cycles of population models with periodic carrying capacity. J. Difference Eq. Appl. 10(8), 791-793.
20. Kon, R. (2001). Attenuant cycles of population models with periodic carrying capacity. J. Difference Eq. Appl., 11(4-5), 423-430.
21. Kot, M. (2001). Elements of Mathematical Ecology, Cambridge University Press, United Kingdom, first edition.
22. Lasota, A. and Mackey, M. C. (1994). Chaos, Fractals and Noise-Stochastic Aspects of Dynamics, Applied Mathematical Sciences, Vol. 97. Springer, New York, second edition.
23. Liu, P. D., and Qian, M. (1995)/ Smooth Ergodic Theory of Random Dynamical Systems, Lecture Notes in Mathematics 1606, Springer, New York.
24. Neave, F. (1953). Principles affecting the size of pink and chum salmon populations in British Columbia. J. Fisheries Res. Board Canada 9, 450-491.
25. Vellekoop, M. H., and Högnäs, G. (1997). A unifying framework for chaos and stochastic stability in discrete population models. J. Math. Biol. 35, 557-588.