High Dimensional Complexity of Dynamical System in the Big Data

Big data technologies are playing an important role in various fields such as biology, finance, economics and engineering. However, the complexity of big data has not been fully understood, especially for the dynamical system in high dimensional space. Here we present a theorem about existence of three-dimensional chaotic behavior for a dynamical system which is widely used in engineering and business. We also give the chaotic behavior at different velocities under initial and fixed values. Simulation results show that our approach can uncover the rich dynamical behaviors of the high dimensional system, e.g. the relationship between the initial value and the chaotic behavior in three- and two-dimensional space.