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In this paper we present a geo-numerical approach for classifying fixed points of the set of ordinary differential equations (ODEs) that represent the reduced model of the cubic-quintic complex Ginzburg–Landau equation (CQ CGL) in a two parameter plane. We will solve the set of ODEs representing the system using the Dormand–Prince method (DOPRI) then by analyzing the final stage of the solution a decision will be made which will result in the classification of solutions into three categories, fixed points, limit cycles or a completely instable solutions, this approach will reveal the variety of solutions and there bifurcation from stable to oscillatory to instable solutions. This study allows us to increase the reliability of the propagation and communication in fiber optic applications. [ABSTRACT FROM AUTHOR]