Analysis of dynamics of classical model single-mode solid-state laser

We considered a model that is described by the system of differential equations of specific type. Since general methods to integrate nonlinear systems of this type do not exist, we use local method of laser dynamics analysis, presupposing initiation of Hopf´s bifurcation, when one of the model parameters becomes the bifurcation value. Comparison of three models of Q-spoiler depending on the photon field density is made. The conclusion from the analysis of these model, is formulated in the following form: transition from one bifurcation parameter to another one in one and the same model is accompanied by some important consequences, in particular the following: contraction or expansion of the interval of stability, a quantity of stationary solutions, change of amplitude and phase of oscillation. In particular cases, this transition may reveal a new problem. This problem may be formulated in the following words: what kind of dependence should exist between the trace of Jacoby´s matrix and the equation to set the stationary solutions of the specified system, to make the following equation true: the derivative of real part of secular value of Jacoby´s matrix by bifurcation parameter is equal to the derivative by x_c of function, which roots are the stationary solutions.