Before revision: We analyze a non-symmetric feedback module being an extension for the repressilator, the first synthetic biological oscillator, which was invented by Elowitz and Leibler. We propose an alternative approach to model the dynamical behaviors  , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.
After revision: We study an alternative approach to model the dynamical behaviors , that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take account to inherent variability of gene expression.