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Global asymptotic stability of a periodic system of delay logistic equations

Published online by Cambridge University Press:  17 April 2009

R.A. Ahlip  and
R.R. King
R.A. Ahlip
Affiliation:
Department of Mathematical SciencesFaculty of Business and TechnologyUniversity of Western Sydney (Macarthur)Cambelltown, NSW 2560Australia
R.R. King
Affiliation:
Department of Mathematical SciencesFaculty of Business and TechnologyUniversity of Western Sydney (Macarthur)Cambelltown, NSW 2560Australia
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Abstract

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Sufficient conditions are obtained for the existence and global asymptotic stability of a periodic solution in Volterra's population system of integrodifferential equations with periodic coefficients. It is shown that if (i) the intraspecific negative feedbacks are instantaneous and dominate the interspecific effects (ii) the minimum possible growth rates are stronger than the maximum interspecific effects weighted with the respective sizes of all species, when they are near their potential maximum sizes, then the system of integrodifferential equations has a unique componentwise periodic solution which is globally asymptotically stable.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 53 , Issue 3 , June 1996 , pp. 373 - 389
Copyright
Copyright © Australian Mathematical Society 1996

References

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