Amplitude equations for time-dependent solutions of the McKendrick equations (Q2783728)
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scientific article; zbMATH DE number 1730705
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Amplitude equations for time-dependent solutions of the McKendrick equations |
scientific article; zbMATH DE number 1730705 |
Statements
17 April 2002
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Hopf bifurcation
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multiple scales analysis
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integro-differential equations
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complex Landau-Stuart equation
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codimension two bifurcation
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Amplitude equations for time-dependent solutions of the McKendrick equations (English)
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This paper is devoted to the study of an age-dependent population modeled by the McKendrick equation. Such equations arise from a conservation law including constitutive assumptions concerning maternity and mortality rates. A weakly nonlinear analysis near neutral stability is made giving bifurcation to time-dependent solutions whose amplitude is governed by a complex Landau-Stuart equation. The multiple scales method is used here. Many different asymptotic behaviors are possible. A delay is introduced yielding a codimension two bifurcation in the system.
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