New Parametric Approach for the General Lorenz System

Abstract: We are concerned with the study of the system of coupled equations of motion for a system of two-level atoms interacting with a single-mode field in the laser cavity on resonance. The passage from the equation of motion to the Lorenz equations is established. Some theoretical aspects of the slowly time -varying phenomena in cavities are discussed and the linear stability analysis is presented. A new approach to solve this nonlinear coupled differential equations is explored and its generalization to the case of variable coefficients is performed.