Picture of a black hole

Strathclyde Open Access research that creates ripples...

The Strathprints institutional repository is a digital archive of University of Strathclyde's Open Access research outputs. Strathprints provides access to thousands of research papers by University of Strathclyde researchers, including by Strathclyde physicists involved in observing gravitational waves and black hole mergers as part of the Laser Interferometer Gravitational-Wave Observatory (LIGO) - but also other internationally significant research from the Department of Physics. Discover why Strathclyde's physics research is making ripples...

Strathprints also exposes world leading research from the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

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

[img]
Preview
PDF (strathprints004545.pdf)
strathprints004545.pdf

Download (266kB) | Preview

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.