Condensed Matter Physics, 2010, vol. 13, No. 1, p. 13001:1-18

Title: Canonical-dissipative limit cycle oscillators with a short-range interaction in phase space
  S. Mongkolsakulvong (Faculty of Science, Department of Physics, Kasetsart University, Bangkok 10900, Thailand) ,
  T.D. Frank (Center for the Ecological Study of Perception and Action, Department of Psychology, University of Connecticut, 406 Babbidge Road, Unit 1020, Storrs, CT 06269, USA)

We consider limit cycle oscillators in terms of canonical-dissipative systems that exhibit a short-range interaction in velocity and position space as described by the Dirac delta function. We derive analytical expressions for stationary distribution functions in phase space and energy space and propose a numerical simulation scheme for the simulation of the many body system as well. We show that the short-range interaction squeezes or stretches energy distribution functions depending on whether the interaction can be regarded as attractive or repulsive. In addition to the interaction effect, we show that energy distribution functions become narrower when limit cycle attractors become stronger. Finally, energy distributions become broader when the pumping energy is increased. The latter effect however disappears in the high energy domain.

Key words: canonical-dissipative systems, Haissinski equation, Tsallis entropy, nonequilibrium systems, nonlinear Fokker-Planck equations
PACS: 05.40.-a, 05.45.Tp, 29.27.Bd, 41.75.-i

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