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

Bifurcation and stability of periodic solutions of differential equations with state-dependent delays
Bifurcation and stability of periodic solutions of differential equations with state-dependent delays
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.
0956-7925
3-14
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b
Schley, D.
3d807658-2cfd-40e6-90ba-5032f88bb54b

Schley, D. (2003) Bifurcation and stability of periodic solutions of differential equations with state-dependent delays. European Journal of Applied Mathematics, 14, 3-14. (doi:10.1017/S0956792502005053).

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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.

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Published date: 2003

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Local EPrints ID: 29288
URI: http://eprints.soton.ac.uk/id/eprint/29288
ISSN: 0956-7925
PURE UUID: 9c20cad8-6eb1-45cd-9879-4cfb4f561419

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Date deposited: 12 May 2006
Last modified: 27 Apr 2022 11:08

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Author: D. Schley

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