Abstract

In this work, we apply a modified box-counting method to estimate the fractal dimension $D$ of a chaotic attractor $E$ generated by a two-dimensional mapping. The obtained numerical results show that the computed value of the capacity dimension $(d_{cap})$ tends to a limit value when the number of points $(n=card(E))$ increases. The function which fits the points $(n,D(n))$ has a sigmoidal form, and its expression characterizes the capacity dimension of chaotic attractors related to different discrete dynamical systems.

Keywords: Dynamical system; chaotic attractor; fractal set; capacity dimension; information dimension.

MSC: 37D45, 37L30, 65D10, 65Y20, 28A80.

Pages:  93$-$101     

Volume  63 ,  Issue  2 ,  2011