OSCILLATORY DYNAMICS INDUCED BY MULTI-DELAYS IN GENE EXPRESSION

We discuss the existence of Hopf bifurcation, the dynamical stability breaking of the molecular concentrations of two generic biochemical reaction systems and their sensitivity to the changes of the parameters incorporated in the model equations. It is found that the oscillatory dynamics can be expected for the systems due to the inclusion of time delays. The chaotic dynamics and the periodic windows in the chaotic domains can exist in the case of the system with two time delays. The proposed mathematical method may have the significance in the problems where the negative and/or positive feedback dynamics, as well as the time delays have the characteristic physical and biological background.