The paper presents a mathematical model of the trigger switching of lambda phage genome on the basis of the molecular ideas by Ptashne. The sigmoid character of the gene cro promotor was explained via lambda-repressor concentration. The temperature switching of genetic trigger was attributed to the existence of permissive and restrictive temperatures by means of the Fokker-Plank probability density formalism. The dependence of the lambda repressor average concentration of the UV-radiation dose was theoretically calculated. For the lambda phage mutant the hysteresic dependence of the lambda repressor and cro concentrations on the external parameters (for example, UV-intensity) was obtained.