In recent years, scholars have studied the chaotic behavior in the fractional dynamic systems and found that the fractional dynamic systems have unique properties that the integer dynamic systems do not have. Therefore, the numerical simulation of fractional chaotic systems is very important. This paper introduces a high-precision numerical method for the fractional-order Rössler chaotic systems. Complex dynamic behavior of the fractional-order Rössler chaotic systems is shown by using the present method. We observe some novel dynamic behaviors in numerical simulation which are unlike any that have been previously found in numerical experiments or theoretical studies. The simulation results of numerical experiments demonstrate the effectiveness of the present method.

近年来，学者们对分数动力系统的混沌行为进行了研究，发现分数动力系统具有整数动力系统所不具备的独特性质。因此，分数阶混沌系统的数值模拟非常重要。本文介绍了分数阶 Rössler 混沌系统的高精度数值方法。使用本方法展示了分数阶 Rössler 混沌系统的复杂动态行为。我们在数值模拟中观察到一些新颖的动态行为，这些行为不同于以前在数值实验或理论研究中发现的任何行为。数值实验的仿真结果证明了该方法的有效性。