Algorithms for asymptotic and numerical modeling of oscillatory modes in the simplest ring of generators with asymmetric nonlinearity

A system of three ring-connected 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 volt-ampere characteristic of this element has a $S$-shaped character. The nonlinear coupling between the generators is organized in such 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 solutions branching from equilibrium states is studied by asymptotic methods. And then the initial system is investigated by numerical methods. The dependence of the system dynamics on the degree of asymmetry of cubic nonlinearity describing the characteristic of a nonlinear element is studied.