### Abstract

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.

Original language | English |
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Pages (from-to) | 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 |

### Keywords

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

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## Cite this

Berkolaiko, G., & Grinfeld, M. (2006). Multiplicity of periodic solutions in bistable equations.

*Proceedings A: Mathematical, Physical and Engineering Sciences*,*462*(2067), 1001-1019. https://doi.org/10.1098/rspa.2005.1601