The influence of external noise on the dynamics of coexisted attractors is investigated in a both discontinuous and noninvertible map. It has coexisted period 5 and period 6 attractors under the parameter range we are interested. The result shows that very week noise has no effect on the coexisted attractors. Under a critical noise strength, one of the two attractors is eliminated, and another attractor leaves stable. Which one of the attractor will be eliminated at this critical noise depends on the control parameter. The previous mentioned mono-stable state changes into chaotic state when the noise strength reached a higher critical value. Therefore, the critical noise strength at which one of the coexisted attractors disappears or a mono-stable state loses it stability could be used to describe the robustness of the attractor.The critical noise strengths at which the two period attractors lose their stability divide the parameter space spanned by the noise strength D and the control parameter μ into four regions.

piece-wise linear map; coexistence of attractors; dynamic transition due to noise