Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-22T07:13:30.494Z Has data issue: false hasContentIssue false
  • English
  • Français

Exchange of equilibria in two species Lotka-Volterra competition models

Published online by Cambridge University Press:  17 February 2009

K. Gopalsamy
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Sufficient conditions are obtained for the existence of a unique asymptotically stable periodic solution for the Lotka-Volterra two species competition system of equations when the intrinsic growth rates are periodic functions of time.

Type
Research Article
Information
The ANZIAM Journal , Volume 24 , Issue 2 , October 1982 , pp. 160 - 170
Copyright
Copyright © Australian Mathematical Society 1982

References

[1]Boyce, M. S. and Daley, D. J., “Population tracking of fluctuating environments and natural selection for tracking ability”, Amer. Natur. 115 (1980), 480–491.CrossRefGoogle Scholar
[2]Coleman, B. D., “Nonautonomous logistic equations as models of the adjustment of populations to environmental change”, Math. Biosci. 45 (1979), 159–173.CrossRefGoogle Scholar
[3]Coleman, B. D., Hsieh, Y. H. and Knowles, G. P., “On the optimal choice of r for a population in a periodic environment”, Math. Biosci. 46 (1979), 71–85.Google Scholar
[4]Cushing, J. M., “Periodic time-dependent predator-prey systems”, SIAM J. Appl. Math. 32 (1977), 82–95.CrossRefGoogle Scholar
[5]Cushing, J. M., “Two species competition in a periodic environment”, J. Math. Biol. (to appear).Google Scholar
[6]Gopalsamy, K., “Limit cycles in periodically perturbed population systems”, Bull. Math. Biol. (to appear).Google Scholar
[7]Krasnoselskii, M. A., “Translation along trajectories of differential equations”, Amer. Math. Soc. Traitsl. 19 (1968).Google Scholar
[8]Massera, J. L., “The existence of periodic solutions of differential equations”, Duke Math. J. 17 (1950), 457–475.CrossRefGoogle Scholar
[9]de Mottoni, P. and Schiaffino, A., “Competition systems with periodic coefficients: a geometric approach”. (to appear).Google Scholar
[10]Nisbet, R. M. and Gurney, W. S. C., “Population dynamics in a periodically varying environment”, J. Theoret. Biol. 56 (1976), 459–475.Google Scholar
[11]Rosenblat, S., “Population models in a periodically fluctuating environment”, J. Math. Biol. 9 (1980), 23–36.CrossRefGoogle Scholar