Approximate solutions of Maxwell Bloch equations and possible Lotka-Volterra type behavior (Q619522)

Real versions of the Maxwell-Bloch equations describing a single-mode class C laser are considered. Chaotic regimes in these equations are studied numerically by calculating the dependence of the Lyapunov exponents on different equations parameters. Hopf bifurcations of the stationary solutions are located in the parameter space. Some special solutions of the model equations are obtained by using subsidiary conditions that allow to reduce the original set of three ordinary differential equations to a system of two differential equations. The connection of the reduced equations to the Lotka-Volterra equations and oscillatory behavior of the Maxwell-Bloch equations in the absence of dissipative terms are discussed.