Multiplicity of periodic solutions in bistable equations

Details Multiplicity of periodic solutions in bistable equations Multiplicity of periodic solutions in bistable equations

2003-10-30

arxiv.org/abs/cond-mat/0310735v2

Proc. Roy. Soc. A 462 (2006) 1001-1019

Physics

Condensed Matter

Statistical Mechanics

Fixed typos; added and reordered figures. 18 pages, 6 figures. An animation of orbits is available at http://www.maths.strat

Scientific paper

10.1098/rspa.2005.1601

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 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.

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