This study focuses on spiral orbits approaching the origin of two-dimensional nonautonomous nonlinear systems. The main result explains that the fractal dimensions (box-counting dimensions) of spiral orbits of the systems on the phase plane can be derived from the power of the nonlinear term. The examples given show that when the coefficients are power functions, the balance between their power and the power of the nonlinear term determines the fractal dimension. In addition, some numerical simulations are also included.

中文翻译：

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非线性对二维微分系统螺旋轨道计盒维数的影响

本研究重点关注接近二维非自治非线性系统原点的螺旋轨道。主要结果说明相平面上系统螺旋轨道的分形维数（盒数维数）可以从非线性项的幂中推导出来。给出的例子表明，当系数是幂函数时，它们的幂与非线性项的幂之间的平衡决定了分形维数。此外，还包括一些数值模拟。