Numerical investigation of instabilities of waves and oscillations in nonlinear gyromagnetic structures with the use of bifurcation points of the nonlinear maxwell operator

Abstract

A method is proposed for bifurcation analysis of electrodynamic structures containing nonlinear media. The method uses bifurcation points of the nonlinear Maxwell operator for a 3D electrodynamic problem. A computational algorithm is developed for analyzing bifurcation points of the nonlinear Maxwell operator. The algorithm involves linearization of nonlinear electrodynamic systems with distributed gyromagnetic inclusions. The method of universal autonomous blocks with virtual Floquet channels and a characteristic determinant are applied to investigate a linearized system. Nonlinear and parametric oscillations in a resonator structure with a ferrite inclusion are analyzed numerically by means of the computational algorithm for analysis of bifurcation points of the nonlinear Maxwell operator.