Roman Voliansky, Nina Volianska, Aji Prasetya Wibawa
The paper deals with the design of backgrounds to study and construct coupled single and multichannel dynamical systems. Our studies are based on considering the motion equations of the known dynamical systems and defining interrelations between these systems. Such an approach allows the transformation of one class of time-variant systems into a time-invariant one, and motion analysis for them can be performed using the known control theory methods. We study the motions of each subsystem and consider their trajectory variations to define the system’s perturbed motions. The motions’ equations can be determined by taking into account the system model and differentiating the perturbed motion coordinates. Such an approach allows us to define system dynamics as a function of the perturbed motion coordinates and their derivatives only and does not require solving equations of the initial system. The coupled system perturbed motion differs from the initial ones and allows us to consider the perturbed motion’s dynamical systems as novel systems. Our method is proven by considering the well-known Duffing pendulum as the subsystem in a coupled dynamical system. © 2025 Copyright for this paper by its authors.
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”, Beresteiskyi Ave., 37, Kyiv, 03056, Ukraine; Taras Shevchenko National University of Kyiv, Bohdan Havrylyshyn Str., 24, Kyiv, 04116, Ukraine; State University of Malang, Jl. Cakrawala No.5, Sumbersari, Kec. Lowokwaru, Jawa Timur, Kota Malang, 65145, Indonesia
