### Abstract

Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

Original language | English |
---|---|

Pages (from-to) | 291-299 |

Number of pages | 9 |

Journal | Bulletin of Mathematical Biology |

Volume | 37 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 1975 |

### Fingerprint

### ASJC Scopus subject areas

- Agricultural and Biological Sciences(all)
- Pharmacology
- Neuroscience(all)
- Mathematics(all)
- Immunology
- Environmental Science(all)
- Computational Theory and Mathematics
- Biochemistry, Genetics and Molecular Biology(all)

### Cite this

*Bulletin of Mathematical Biology*,

*37*(3), 291-299. https://doi.org/10.1007/BF02461447

**Estimates of predator-prey limit cycles.** / De Angelis, Donald L.

Research output: Contribution to journal › Article

*Bulletin of Mathematical Biology*, vol. 37, no. 3, pp. 291-299. https://doi.org/10.1007/BF02461447

}

TY - JOUR

T1 - Estimates of predator-prey limit cycles

AU - De Angelis, Donald L.

PY - 1975/6/1

Y1 - 1975/6/1

N2 - Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

AB - Perturbation methods are applied to a differential equation predator-prey model to find the approximate amplitudes and period of limit cycle solutions. In the model the feeding rate per unit predator per unit prey decreases as the prey become scare. The rigorous applicability of the perturbation technique depends on the assumptions that the limit cycle amplitude is relatively small and that near the equilibrium point the growth rate of each species is most sensitive to changes in the density of the other species. The second assumption is usually roughly satisfied in practice and examples are considered which suggest that the first assumption can be greatly relaxed.

UR - http://www.scopus.com/inward/record.url?scp=0016812704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0016812704&partnerID=8YFLogxK

U2 - 10.1007/BF02461447

DO - 10.1007/BF02461447

M3 - Article

VL - 37

SP - 291

EP - 299

JO - Bulletin of Mathematical Biology

JF - Bulletin of Mathematical Biology

SN - 0092-8240

IS - 3

ER -