Eur. Phys. J. B (2012) 85: 90
https://doi.org/10.1140/epjb/e2012-20720-4

Regular Article

Oscillatory nonequilibrium Nambu systems: the canonical-dissipative Yamaleev oscillator

¹ Faculty of Science, Department of Physics, Kasetsart University, 10900 Bangkok, Thailand
² Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Storrs, 06269 CT, USA
³ Systems Biology Ireland, University College Dublin, Belfield, 4 Dublin, Ireland
⁴ UCD School of Physics, University College Dublin, Belfield, 4 Dublin, Ireland

^a e-mail: till.frank@uconn.edu

Received: 31 August 2011
Received in final form: 14 January 2012
Published online: 7 March 2012

Abstract

We study the emergence of oscillatory self-sustained behavior in a nonequilibrium Nambu system that features an exchange between different kinetical and potential energy forms. To this end, we study the Yamaleev oscillator in a canonical-dissipative framework. The bifurcation diagram of the nonequilibrium Yamaleev oscillator is derived and different bifurcation routes that are leading to limit cycle dynamics and involve pitchfork and Hopf bifurcations are discussed. Finally, an analytical expression for the probability density of the stochastic nonequilibrium oscillator is derived and it is shown that the shape of the density function is consistent with the oscillator properties in the deterministic case.