Singular perturbation analysis and gene regulatory networks with delay

The problem of how the dynamics of the smooth gene networks is related to the simplified dynamics of the Boolean networks is studied. The emphasis is put on the gene regulatory networks with delay. Asymptotic analysis which is applied in the paper goes back to Tikhonov’s theory of singular perturbed differential equations and a modified algorithm of reducing delay equations to ordinary differential equations. A number of illustrative examples complements the theory which is offered in the paper.