Abstract: Nonlinear problems in chemical dynamics have fascinated engineers and scientists since 1950s. Notable among such problems are those of stabilities of reaction and control system design. Attempts to elaborate on the dynamic behavior and reach the optimal performance led to the studies of bifurcation and chaos: the highly nonlinear characteristics on the verge of instability. The studies on bifurcation and chaos problems have been, since the middle of 1970s, carried out in the fields of reaction and control engineering. Some of the approaches demonstrated in bifurcation theory are extremely important to the stability design of reaction: dissipative system, fluid bed reactor, polymerization reaction system, and corresponding control systems.