### Abstract

Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

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

Article number | 008 |

Pages (from-to) | 653-669 |

Number of pages | 17 |

Journal | Nonlinearity |

Volume | 1 |

Issue number | 4 |

DOIs | |

State | Published - 1988 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Mathematical Physics
- Statistical and Nonlinear Physics
- Applied Mathematics
- Mathematics(all)

### Cite this

*Nonlinearity*,

*1*(4), 653-669. [008]. https://doi.org/10.1088/0951-7715/1/4/008

**Some cubic systems with several limit cycles.** / Lloyd, N. G.; Blows, Terence R; Kalenge, M. C.

Research output: Contribution to journal › Article

*Nonlinearity*, vol. 1, no. 4, 008, pp. 653-669. https://doi.org/10.1088/0951-7715/1/4/008

}

TY - JOUR

T1 - Some cubic systems with several limit cycles

AU - Lloyd, N. G.

AU - Blows, Terence R

AU - Kalenge, M. C.

PY - 1988

Y1 - 1988

N2 - Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

AB - Two-dimensional systems x=P(x, y), y=Q(x,y) in which P and Q are cubic polynomials, are considered, and a number of classes with several limit cycles are described. Examples of systems with six small-amplitude limit cycles are given. Other classes of systems with several limit cycles are obtained by considering simultaneous bifurcation from a finite critical point and infinity. Simultaneous bifurcation from several critical points is investigated.

UR - http://www.scopus.com/inward/record.url?scp=0000878257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000878257&partnerID=8YFLogxK

U2 - 10.1088/0951-7715/1/4/008

DO - 10.1088/0951-7715/1/4/008

M3 - Article

AN - SCOPUS:0000878257

VL - 1

SP - 653

EP - 669

JO - Nonlinearity

JF - Nonlinearity

SN - 0951-7715

IS - 4

M1 - 008

ER -