Numerical Analysis of Electromagnetic Wave Instability in Nonlinear Ferrite Structures Using Bifurcation Points of the Nonlinear Maxwell ¢??s Operator

In this paper a new method for rigorous modeling of nonlinear phenomena due to the instability in 3-D ferrite structures was developed based on the numerical analysis of the bifurcation points of the nonlinear Maxwell´s operator. This technique, originating in the mathematical theory of differentiable maps and the bifurcation theory, is a pioneering approach in electrodynamics. The bifurcation points were determined by our computational algorithm, using the eigenvalues of the matrix resulting from the linearized Maxwell´s operator, and the onset and the breakdown of self-oscillations in the ferrite resonator structures, caused by the instability, were modeled.