Multiplicity of periodic solutions in bistable equations
| dc.creator | Berkolaiko, Gregory | |
| dc.creator | Grinfeld, Michael | |
| dc.date | 2003-10-30 | |
| dc.date | 2004-01-14 | |
| dc.date.accessioned | 2026-07-07T06:27:36Z | |
| dc.date.available | 2026-07-07T06:27:36Z | |
| dc.description | 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. | |
| dc.description | Fixed 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.identifier | https://arxiv.org/abs/cond-mat/0310735 | |
| dc.identifier | http://arxiv.org/abs/cond-mat/0310735 | |
| dc.identifier | Proc. Roy. Soc. A 462 (2006) 1001-1019 | |
| dc.identifier | doi:10.1098/rspa.2005.1601 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/97456 | |
| dc.subject | Statistical Mechanics | |
| dc.subject | Classical Analysis and ODEs | |
| dc.title | Multiplicity of periodic solutions in bistable equations | |
| dc.type | text |