Multiplicity of periodic solutions in bistable equations

dc.creatorBerkolaiko, Gregory
dc.creatorGrinfeld, Michael
dc.date2003-10-30
dc.date2004-01-14
dc.date.accessioned2026-07-07T06:27:36Z
dc.date.available2026-07-07T06:27:36Z
dc.descriptionWe 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 the time-varying external magnetic field. When the strength of the external field is varied, the set of periodic solutions undergoes a bifurcation in both equations. We prove that despite profound 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 strength of the magnetic field.
dc.descriptionFixed typos; added and reordered figures. 18 pages, 6 figures. An animation of orbits is available at http://www.maths.strath.ac.uk/~aas02101/bistable/
dc.identifierhttps://arxiv.org/abs/cond-mat/0310735
dc.identifierhttp://arxiv.org/abs/cond-mat/0310735
dc.identifierProc. Roy. Soc. A 462 (2006) 1001-1019
dc.identifierdoi:10.1098/rspa.2005.1601
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/97456
dc.subjectStatistical Mechanics
dc.subjectClassical Analysis and ODEs
dc.titleMultiplicity of periodic solutions in bistable equations
dc.typetext

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