In this paper,  the Majda analog system in the form of ZND detonation is built. the selected ignition function is more general than before. and the Arrhenius  reaction equation is used to study the detonation stability. The main research content are as follows:

1 .In the extreme case(the simulated activation energy parameter is equal to zero), a relatively simple analog system was obtained and studied. Using the direct calculation method, the traveling wave solutions of the analog system and the steady-state detonation structure are obtained. The steady state detonation wave is added with perturbation to study the stability of detonation. Through the stability analysis of the normal mode, the determinant of the stability of the limiting perturbation propagation(Evans-Lopatinski determinant ) and the determination principle of the stability are obtained. The detonation under the extreme conditions is stable through the direct calculation method, and a stable detonation perturbation oscillation pattern is obtained.

2. In the normal case(the simulated activation energy parameter is  not equal to zero),  the Arrhenius reaction equation is more complex and cannot be calculated directly. For such a model, a detonation steady-state solution is obtained by using a numerical calculation method, and stability determination is performed using a stability determinant. Since the solution is non-analytic, the stability determinant cannot be calculated directly. The winding number method is introduced to determine the stability. The one-dimensional detonation stability of the analog system under different parameters was obtained, and the physical rationality of the results were analyzed.