Algorithms for Asymptotic and Numerical Modeling of Oscillatory Modes in the Simplest Ring of Generators with Asymmetric Nonlinearity

Abstract

A system of three ring-coupled generators with asymmetric nonlinearity and special nonlinear coupling is considered. The investigated system simulates an electrical circuit of three identical generators. Each generator is an oscillatory circuit with a nonlinear element. The current–voltage characteristic of this element has the S-shape. The nonlinear coupling between the generators is organized in such a way that it has a transmission coefficient close to one in the forward direction and close to zero in the reverse direction. First, the problem of finding the solutions that bifurcate from equilibrium states is investigated by asymptotic methods. Then, the original system is studied by numerical methods. The dependence of the dynamics of the system on the degree of asymmetry of cubic nonlinearity, which describes the characteristic of the nonlinear element, is analyzed.