Multiplicity of periodic solutions in bistable equations
Berkolaiko, Gregory and Grinfeld, Michael (2006) Multiplicity of periodic solutions in bistable equations. Proceedings A: Mathematical, Physical and Engineering Sciences, 462 (2067). pp. 1001-1019. ISSN 1471-2962
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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.
Creators(s): | Berkolaiko, Gregory and Grinfeld, Michael; | Item type: | Article |
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ID code: | 4545 |
Keywords: | bistability, suzuki-kubo equation, mathematics, bistable systems, Mathematics, Physics and Astronomy(all), Engineering(all), Mathematics(all) |
Subjects: | Science > Mathematics |
Department: | Faculty of Science > Mathematics and Statistics > Mathematics Faculty of Science > Mathematics and Statistics |
Depositing user: | Strathprints Administrator |
Date deposited: | 23 Jul 2008 |
Last modified: | 20 Jan 2021 17:30 |
URI: | https://strathprints.strath.ac.uk/id/eprint/4545 |
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