Abstract
This paper considers the oscillators coupled in the form of a ring through resistors. It is described for the case of five oscillators that, for the symmetrical solutions, the analysis based on the conjugate class in group theory is useful. Major problems in the coupled oscillators are the existence of the synchronized periodic solution and its stability. In the case of the weakly nonlinear system, the problems of the synchronized periodic solution and the stability are almost answered by techniques that include mode analysis. In the case of the strongly nonlinear system, on the other hand, the periodic solutions with symmetry have been classified mostly based on the subgroup in the group theory when the number of coupled oscillators is less. When the number of oscillators is increased, however, the number of subgroups becomes tremendous, which makes systematic analysis difficult. This paper uses the conjugate class and shows that the symmetrical solutions can be classified systematically. It is also shown that the approximate periodic solution with symmetry can be approximately determined by the averaging based on the symmetry.