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Multiplicity of periodic solutions in bistable systems

Berkolaiko, G. and Grinfeld, M. (2006) Multiplicity of periodic solutions in bistable systems. Proceedings A: Mathematical, Physical and Engineering Sciences, 462 (2067). pp. 1001-1019. ISSN 1364-5021

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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.

Item type: Article
ID code: 4545
Keywords: bistability, suzuki-kubo equation, mathematics, bistable systems, Mathematics
Subjects: Science > Mathematics
Department: Faculty of Science > Mathematics and Statistics
Faculty of Science > Mathematics and Statistics > Mathematics
Depositing user: Strathprints Administrator
Date Deposited: 23 Jul 2008
Last modified: 20 Oct 2015 19:33

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