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
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.
Key words: Statistical and Nonlinear Physics
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2012