Macroscopic asymptotic property from Stuart-landau oscillator to phase oscillator - a case of the third order Stuart-landau equation

摘要

Solvable models of oscillator associative memory can be classified into two models: one consisting of phase oscillators and the other composed of Stuart-Landau (SL) oscillators. It is well-known in a microscopic level that, when the mutual interaction of a SL oscillator system is sufficiently weak, the SL system can be reduced to a phase system by the multi-scale perturbation method. In this paper, I study macroscopic relationship between a SL system and phase system. By using the replica method, I derive macroscopic order parameter equations which describe the macroscopic, properties of both the systems. Then I evaluate macroscopic asymptotic properties from the SL system to the phase system, when the temperature is finite and infinitesimal.