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Bifurcation and stability of periodic solutions of differential equations with state-dependent delays

Published online by Cambridge University Press:  17 March 2003

D. SCHLEY
D. SCHLEY
Affiliation:
Department of Medical Physics & Bioengineering, Southampton General Hospital, Southampton, Hampshire SO16 6YD, UK
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Abstract

We consider periodic solutions which bifurcate from equilibria in simple population models which incorporate a state-dependent time delay of the discrete kind. The delay is a function of the current size of the population. Solutions near equilibria are constructed using perturbation methods to determine the sub/supercriticality of the bifurcation and hence their stability. The stability of the bifurcating solutions depends on the qualitative form of the delay function. This is in contrast to the stability of an equilibrium, which is determined purely by the actual value of this function at the equilibrium.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 14 , Issue 1 , February 2003 , pp. 3 - 14
Copyright
2003 Cambridge University Press

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