Under different demand patterns, the dynamic behaviors of nonlinear supply chain system constrained by limited supply capacity and forbidden returns are studied. By calculating the maximum Lyapunov exponent, the quasi- chaotic behavior is analyzed under different scenarios of supply chain systems. The study demonstrates that the constrained supply chain system has more complex dynamic characters, but some regular rules can be concluded. Even in the random demand pattern, if ordering policy is reasonable, the chaotic behavior can be mitigated or even avoided. On the contrary, under the certain demand pattern, unreasonable ordering policies would lead to chaotic behaviors of the supply system. The experimental results show the reasonability of the conclusion.