TY - JOUR AU - A. Yu. Kolesov AU - N. Kh. Rozov PY - 2013/01/25 Y2 - 2024/03/28 TI - New methods for the investigation of periodic solutions in ring systems of unidirectionally coupled oscillators JF - Ukrains’kyi Matematychnyi Zhurnal JA - Ukr. Mat. Zhurn. VL - 65 IS - 1 SE - Research articles DO - UR - https://umj.imath.kiev.ua/index.php/umj/article/view/2406 AB - We consider special systems of ordinary differential equations, namely, ring systems of unidirectionally coupled oscillators.A new method is developed for the investigation of the problem of the existence and stability of periodic solutions for thisclass of systems. The specific feature of this approach is the use of certain auxiliary delay systems for the determination ofcycles and for the analysis of their properties. The proposed method is illustrated by a specific example. ER -