The twin-stripe laser is an important type of monolithic lasers. Based on the rate equations, the nonlinear dynamic behaviors for the twin-stripe laser are analyzed by the numerical method. The transient responses are elaborately discussed for the twin-stripe laser with two kinds of different guidance mechanisms, and initial phase difference under different bias configurations. It is concluded that the instability/chaos is the intrinsic operation of the twin-stripe laser. Either phase-locked operation without detuning or stable output with two-wavelength only can be obtained under certain running conditions besides the special structure design.