Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-23T10:52:52.005Z Has data issue: false hasContentIssue false
  • English
  • Français

Harmless delays in a periodic ecosystem

Published online by Cambridge University Press:  17 February 2009

K. Gopalsamy
K. Gopalsamy
Affiliation:
School of Mathematics, Flinders University, Bedford Park, S.A. 5042.
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 linearly asymptotically stable positive periodic solution of an ecosystem model of two species competition in a periodic environment with time lags in interspecific interactions. It is shown that if the self-regulating intraspecific interaction effects are strong enough and act without time delays then time delays of any length in the interspecific interactions cannot destabilise an otherwise stable ecosystem in a periodic environment.

Type
Research Article
Information
The ANZIAM Journal , Volume 25 , Issue 3 , January 1984 , pp. 349 - 365
Copyright
Copyright © Australian Mathematical Society 1984

References

[1]Busenberg, S. and Cooke, K. L., “Periodic solutions of a periodic nonlinear delay differential equation,” SIAM J. Appl. Math. 34 (1978), 704–721.CrossRefGoogle Scholar
[2]Gopalsamy, K. and Aggarwala, B. D., “Limit cycles in two species competition with time delays”, J. Austral. Math. Soc. Ser. B 22 (1980), 148–160.CrossRefGoogle Scholar
[3]Gopalsamy, K.. “Time lags and global stability in two species competition”, Bull. Math. Biol. 42 (1980), 729–737.CrossRefGoogle Scholar
[4]Gopalsamy, K., “Limit cycles in periodically perturbed population systems”, Bull. Math. Biol. 43 (1981), 463–485.CrossRefGoogle Scholar
[5]Gopalsamy, K., “Exchange of equilibria in two species Lotka-Volterra competition”, J. A ustral. Math. Soc. Ser. B 24 (1982), 160–170.CrossRefGoogle Scholar
[6]Gopalsamy, K., “Harmless delays in model systems”, Bull. Math. Biol. (in press).Google Scholar
[7]MacArthur, R., Geographical ecology (Harper and Row, New York, 1972).Google Scholar
[8]Pianka, E. R., Evolutionary ecology (Harper and Row, New York, 1974).Google Scholar
[9]Schmitt, K., “Fixed points and coincidence theorems with applications to nonlinear differential and integral equations”, Rapp. #97, Univ. Catholique de Louvain; Institut de Mathématique Pure et Appliquée, 1976.Google Scholar
[10]Shibata, A. and Saito, N., “Time delays and chaos in two competing species”, Math. Biosci. 51 (1980), 199–211.CrossRefGoogle Scholar
[11]Smith, H., “On periodic solutions of delay integral equations modelling epidemics and population growth”, Ph.D. Dissertation, University of Iowa, 1976.Google Scholar