### Abstract

Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

Original language | English (US) |
---|---|

Pages (from-to) | 2323-2328 |

Number of pages | 6 |

Journal | Computers and Mathematics with Applications |

Volume | 56 |

Issue number | 9 |

DOIs | |

State | Published - Nov 2008 |

### Fingerprint

### Keywords

- Cubic systems
- Hilbert's Sixteenth Problem
- Hopf bifurcation
- Limit cycles

### ASJC Scopus subject areas

- Applied Mathematics
- Computational Mathematics
- Modeling and Simulation

### Cite this

**Small amplitude limit cycles of symmetric cubic systems.** / Blows, Terence R.

Research output: Contribution to journal › Article

*Computers and Mathematics with Applications*, vol. 56, no. 9, pp. 2323-2328. https://doi.org/10.1016/j.camwa.2007.07.020

}

TY - JOUR

T1 - Small amplitude limit cycles of symmetric cubic systems

AU - Blows, Terence R

PY - 2008/11

Y1 - 2008/11

N2 - Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

AB - Hilbert's Sixteenth Problem concerns the number and relative position of limit cycles in a planar polynomial system of differential equations. We show, using multiple Hopf bifurcation from multiple fine foci, that limit cycle configurations of types (3, 3, -2, -2) and (2, 2, 1, 1, -1) occur in symmetric cubic systems.

KW - Cubic systems

KW - Hilbert's Sixteenth Problem

KW - Hopf bifurcation

KW - Limit cycles

UR - http://www.scopus.com/inward/record.url?scp=52049087597&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=52049087597&partnerID=8YFLogxK

U2 - 10.1016/j.camwa.2007.07.020

DO - 10.1016/j.camwa.2007.07.020

M3 - Article

VL - 56

SP - 2323

EP - 2328

JO - Computers and Mathematics with Applications

JF - Computers and Mathematics with Applications

SN - 0898-1221

IS - 9

ER -