Lasko Basnarkov and Viktor Urumov J. Stat. Mech. (2009) P10014 doi:10.1088/1742-5468/2009/10/P10014
Lasko Basnarkov1 and Viktor Urumov2
Show affiliationsWe consider an analytically solvable version of the Winfree model of synchronization of phase oscillators (proposed by Ariaratnam and Strogatz 2001 Phys. Rev. Lett. 86 4278). It is obtained that the transition from incoherence to a partial death state is characterized by third-order or higher phase transitions according to the Ehrenfest classification. The order of the transition depends on the shape of the distribution function for natural frequencies of oscillators in the vicinity of their lowest frequency. The corresponding critical exponents are found analytically and verified with numerical simulations of equations of motion. We also consider the generalized Winfree model with the interaction strength proportional to a power of the Kuramoto order parameter and find the domain where the critical exponent remains unchanged by this modification.
05.45.Xt Synchronization; coupled oscillators
05.70.Fh Phase transitions: general studies
64.60.F- Equilibrium properties near critical points, critical exponents
82C80 Numerical methods (Monte Carlo, series resummation, etc.)
82C26 Dynamic and nonequilibrium phase transitions (general)
Issue 10 (October 2009)
Received 13 August 2009, accepted for publication 2 October 2009
Published 21 October 2009
Lasko Basnarkov and Viktor Urumov J. Stat. Mech. (2009) P10014
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