Abstract
A statistical mechanical theory is presented for the self-organization of a macroscopic oscillation with the presence of external fluctuations in a system of Van der Pol oscillators coupled through dissipative interactions. Starting from Langevin equations for the Van der Pol oscillators, the static and dynamic characteristics are studied. The threshold condition is given by the relative size between the fluctuation and the interaction. The transitions between synchronous and asynchronous phases are well discussed by a Landau-type equation. The steady state value of the order parameter and the onset time are compared between the theory and the computer experiments and a good agreement is obtained.
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Yamaguchi, Y., Kometani, K. & Shimizu, H. Self-synchronization of nonlinear oscillations in the presence of fluctuations. J Stat Phys 26, 719–743 (1981). https://doi.org/10.1007/BF01010935
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DOI: https://doi.org/10.1007/BF01010935