Influence of nonlinearity to box-counting dimensions of spiral orbits for two-dimensional differential systems

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.