Out-of-time-ordered correlators (OTOCs) are an effective tool in characterizing black hole chaos, many-body thermalization, and quantum dynamics instability. Previous research findings have shown that the OTOCs' exponential growth (EG) marks limit for systems. However, we report this paper a periodically-modulated nonlinear Schr\"odinger system, which interestingly find way of growth: super-EG....