### Abstract

A local two parameter bifurcation theorem concerning the bifurcation from steady states of time periodic solutions of a nonlinear system of partial, integro-differential equations is proved. A Hopf bifurcation theorem is derived as a corollary. By means of independent and dependent variable changes this theorem is applicable to the general McKendrick equations governing the growth of an age-structured population (with the added feature here of a possible gestation period). The theorem is based on a Fredholm theory developed in the paper for the associated linear equations. An application is given to an age-structured population whose fecundity is density and age dependent and it is shown that for a sufficiently narrow age-specific "reproductive and resource consumption window" steady state instabilities, accompanied by sustained time periodic oscillations, occur when the birth modulus surpasses a critical value.

Original language | English (US) |
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Pages (from-to) | 459-478 |

Number of pages | 20 |

Journal | Computers and Mathematics with Applications |

Volume | 9 |

Issue number | 3 |

DOIs | |

State | Published - 1983 |

### ASJC Scopus subject areas

- Modeling and Simulation
- Computational Theory and Mathematics
- Computational Mathematics