Hopf bifurcation in a structured population model for the sexual phase of monogonont rotifers |
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Authors: | Calsina Angel Ripoll Jordi |
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Institution: | (1) Departament d'Informàtica i Matemàtica Aplicada, Universitat de Girona, Campus Montilivi, E-17071 Girona, Spain. e-mail: acalsina@ima.udg.es, jripoll@ima.udg.es, ES |
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Abstract: | We are studying a population of monogonont rotifers in the context of non-linear age-dependent models. In the sexual phase
of their reproductive cycle we consider the population structured by age, and composed of three subclasses: virgin mictic
females, mated mictic females, and haploid males. The model system has a unique stationary population density which is stable
as long as a parameter, related to male-female encounter rate, remains below a critical value. When the parameter increases
beyond this critical value, the stationary solution becomes unstable and a stable limit cycle (isolated periodic orbit) appears.
The occurrence of this supercritical Hopf bifurcation is shown analytically.
Received: 2 August 2001 / Revised version: 3 January 2002 / Published online: 26 June 2002 |
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