Infra-red stable fixed points of Yukawa couplings in supersymmetric models

We provide the solutions of the fixed point conditions of the Yukawa sector for a large class of N = 1 supersymmetric theories including the minimal and next-to-minimal supersymmetric standard models and their grand unified and other extensions. We also introduce a test which can discriminate between infra-red stable, infra-red unstable and saddle point solutions, and illustrate our methods with the example of the next-to-minimal supersymmetric standard model. We show that in this case, the fixed point prediction of the top quark mass is equivalent to that of the minimal supersymmetric standard model, supporting previous numerical analyses.