There exists a class of quadratic nonlinear systems with specific turbulent fluctuation excitation types in nature, which belong to a special non- Gaussian input signal system. The characteristic is that the input signal spectrum is generated by turbulent fluctuations, and the power spectrum distribution of this turbulence fluctuation signal is close to Gaussian distribution. Starting from the work of Choi et al. [J. Sound and Vibration 99(1985) 309] and Kim et al. [IEEE J. Ocean. Eng. OE- 12(1987) 568], this article extends the simulation of specific turbulent fluctuation excitation response type quadratic nonlinear systems represented by wave excitation mooring ship response and fully developed turbulence internal development based on bispectral analysis technology, and conducts extended and systematic modeling analysis of the simulation system. The complete iterative method [Phys. Scr. 95(2020) 055202] was applied to solve the model for the first time, and the linear transfer function and quadratic nonlinear transfer function are calculated. The comparison of simulation and modeling results with the real systems and their models confirms the correctness of the results from system simulation, system modeling, and model solving. The results obtained are all in line with expectations. The coherence analysis shows that the quadratic coherence of the random wave-ship swaying system is much greater than the linear coherence, but the linear coherence of the fully developed turbulence is greater for the near Gaussian input type. The reverse computation verification or comparison with re real systems indicates that the turbulence simulation and system modeling methods in this article have good accuracy, with high efficiency in solving algorithms, and the research results can be effectively applied to the model description and system analysis of the quadratic nonlinear systems related to specific turbulent fluctuation excitation response.