### Abstract

Language | English |
---|---|

Pages | 1001-1019 |

Number of pages | 18 |

Journal | Proceedings A: Mathematical, Physical and Engineering Sciences |

Volume | 462 |

Issue number | 2067 |

DOIs | |

Publication status | Published - 8 Mar 2006 |

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### Keywords

- bistability
- suzuki-kubo equation
- mathematics
- bistable systems

### Cite this

*Proceedings A: Mathematical, Physical and Engineering Sciences*,

*462*(2067), 1001-1019. https://doi.org/10.1098/rspa.2005.1601

}

*Proceedings A: Mathematical, Physical and Engineering Sciences*, vol. 462, no. 2067, pp. 1001-1019. https://doi.org/10.1098/rspa.2005.1601

**Multiplicity of periodic solutions in bistable equations.** / Berkolaiko, Gregory; Grinfeld, Michael.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Multiplicity of periodic solutions in bistable equations

AU - Berkolaiko, Gregory

AU - Grinfeld, Michael

PY - 2006/3/8

Y1 - 2006/3/8

N2 - We study the number of periodic solutions in two first-order non-autonomous differential equations, both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in a time-varying external magnetic field. When the amplitude of the external field is increased, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite superficial similarities between the equations, the character of the bifurcation can be very different. This results in a different number of coexisting stable periodic solutions in the vicinity of the bifurcation. As a consequence, in one of the models, the Suzuki-Kubo equation, one can effect a discontinuous change in magnetization by adiabatically varying the amplitude of the magnetic field.

AB - We study the number of periodic solutions in two first-order non-autonomous differential equations, both of which have been used to describe, among other things, the mean magnetization of an Ising magnet in a time-varying external magnetic field. When the amplitude of the external field is increased, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite superficial similarities between the equations, the character of the bifurcation can be very different. This results in a different number of coexisting stable periodic solutions in the vicinity of the bifurcation. As a consequence, in one of the models, the Suzuki-Kubo equation, one can effect a discontinuous change in magnetization by adiabatically varying the amplitude of the magnetic field.

KW - bistability

KW - suzuki-kubo equation

KW - mathematics

KW - bistable systems

U2 - 10.1098/rspa.2005.1601

DO - 10.1098/rspa.2005.1601

M3 - Article

VL - 462

SP - 1001

EP - 1019

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

T2 - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2067

ER -