The integration of deactivation and regeneration often leads to a significant reduction in investment and operating costs. In this work, the stability of the integrated system is analyzed by the Brouwer fix-point theorem, and the transition of the state-variable is simulated by a numerical method. It is found that there is a fix-point in state-space for the integrated system of deactivation and regeneration. The steady-state can finally be attained after the disturbance becomes constant. Furthermore, there are four kinds of transient patterns, i.e., monotone self-stabilization, monotone self-stabilization with dead zone, self-stabilization with reverse characteristic, and damped-oscillation.