Multiplicity of periodic solutions in bistable equations

Gregory Berkolaiko, Michael Grinfeld

Research output: Contribution to journalArticle

2 Citations (Scopus)
108 Downloads (Pure)

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 languageEnglish
Pages (from-to)1001-1019
Number of pages18
JournalProceedings A: Mathematical, Physical and Engineering Sciences
Volume462
Issue number2067
DOIs
Publication statusPublished - 8 Mar 2006

Keywords

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

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