Systems of high-dimensional nonlinear ordinary differential equations play a significant role in Physics and applied sciences including big-data optimization, financial models, epidemic disease models. In this paper, we are concerned with numerical solutions of Bao’s system that is a 4-dimensional hyperchaotic system introduced by Bo-Cheng and Zhong (2008). We solve the Bao’s system with both the Crank-Nicolson and power series methods. Crank-Nicolson method is eventually evolved into a new system whose solution is presented in a quite neat algorithmic manner. By adding standard Brownian motion to each term in the model, we express the Bao’s system as a system of stochastic differential equations. We solve the stochastic system with an Euler-type approximate solution method. By adding noise and expressing time derivatives with Caputo-type fractional derivative, we study on synchronization and parameter estimation of the models. To the best of our knowledge, Bao’s system has not been numerically solved with the methods employed in this paper previously, and this paper considers fractional and stochastic Bao’s system for the first time in the history of research. Techniques employed by us in this paper may serve as a framework for solutions of many other systems of ordinary differential equations including Lorenz types and epidemic models.

高维非线性常微分方程系统在物理学和应用科学中（包括大数据优化，财务模型，流行病模型）起着重要作用。在本文中，我们关注鲍氏系统的数值解，该系统是由Bo-Cheng和Zhong（2008）引入的4维超混沌系统。我们使用Crank-Nicolson方法和幂级数方法来解决Bao的系统。Crank-Nicolson方法最终演变为一个新系统，其解决方案以一种非常简洁的算法方式给出。通过向模型中的每个项添加标准布朗运动，我们将鲍氏系统表示为随机微分方程组。我们用欧拉型近似解法求解随机系统。通过添加噪声并用Caputo型分数导数表示时间导数，我们研究了模型的同步和参数估计。据我们所知，Bao的系统以前并未采用本文所采用的方法进行数值求解，因此本文在研究历史上首次考虑了分数阶和随机的Bao的系统。我们在本文中采用的技术可以作为许多其他常微分方程系统（包括Lorenz类型和流行模型）解的框架。并在研究历史上首次考虑了分数和随机包系统。我们在本文中采用的技术可以作为许多其他常微分方程系统（包括Lorenz类型和流行模型）解的框架。并在研究历史上首次考虑了分数和随机包系统。我们在本文中采用的技术可以作为许多其他常微分方程系统（包括Lorenz类型和流行模型）解的框架。