## Abstract

The general system of differential equations describing predator-prey dynamics is modified by the assumption that the coefficients are periodic functions of time. By use of standard techniques of bifuraction theory, as well as a recent global result of P. H. Rabinowitz, it is shown that this system has a periodic solution (in place of an equilibrium) provided the long term time average of the predator's net, uninhibited death rate is in a suitable range. The bifurcation is from the periodic solution of the time-dependent logistic equation for the prey (which results in the absence of any predator). Numerical results which clearly show this bifurcation phenomenon are briefly discussed.

Original language | English (US) |
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Pages (from-to) | 82-95 |

Number of pages | 14 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 32 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 1977 |

Externally published | Yes |

## ASJC Scopus subject areas

- Applied Mathematics