### Abstract

In this paper the following periodically perturbed autonomous system text omatted in which g is 2π/ω-periodic in t and f(0,η) = 0 is considered. It is assumed that the autonomous system obtained by setting b=0 undergoes a generic Hopf bifurcation from x = 0 at η= 0 and that the frequency,ω, is not in resonance with the frequency of the Hopf periodic solution. Under these conditions, we show that an integral manifold of solutions bifurcates from the unique 2π/ω-periodic solution, x*, of (1) on one side of the neutral stability curve for x* in the (b,η) plane.

Original language | English (US) |
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Pages (from-to) | 173-195 |

Number of pages | 23 |

Journal | Applicable Analysis |

Volume | 12 |

Issue number | 3 |

DOIs | |

State | Published - Jan 1 1981 |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Nonresonant periodic perturbation of the hopf bifurcation.** / Smith, Hal.

Research output: Contribution to journal › Article

*Applicable Analysis*, vol. 12, no. 3, pp. 173-195. https://doi.org/10.1080/00036818108839359

}

TY - JOUR

T1 - Nonresonant periodic perturbation of the hopf bifurcation

AU - Smith, Hal

PY - 1981/1/1

Y1 - 1981/1/1

N2 - In this paper the following periodically perturbed autonomous system text omatted in which g is 2π/ω-periodic in t and f(0,η) = 0 is considered. It is assumed that the autonomous system obtained by setting b=0 undergoes a generic Hopf bifurcation from x = 0 at η= 0 and that the frequency,ω, is not in resonance with the frequency of the Hopf periodic solution. Under these conditions, we show that an integral manifold of solutions bifurcates from the unique 2π/ω-periodic solution, x*, of (1) on one side of the neutral stability curve for x* in the (b,η) plane.

AB - In this paper the following periodically perturbed autonomous system text omatted in which g is 2π/ω-periodic in t and f(0,η) = 0 is considered. It is assumed that the autonomous system obtained by setting b=0 undergoes a generic Hopf bifurcation from x = 0 at η= 0 and that the frequency,ω, is not in resonance with the frequency of the Hopf periodic solution. Under these conditions, we show that an integral manifold of solutions bifurcates from the unique 2π/ω-periodic solution, x*, of (1) on one side of the neutral stability curve for x* in the (b,η) plane.

UR - http://www.scopus.com/inward/record.url?scp=84963429120&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84963429120&partnerID=8YFLogxK

U2 - 10.1080/00036818108839359

DO - 10.1080/00036818108839359

M3 - Article

VL - 12

SP - 173

EP - 195

JO - Applicable Analysis

JF - Applicable Analysis

SN - 0003-6811

IS - 3

ER -