Lyapunov Exponents and Kaplan-yorke Dimension for Fivedimensional System

This work introduces a new high-dimensional five-dimensional system with chaotic and periodic solutions. For special values of parameters, we calculate the Kaplan- Yorke dimension and we show the dynamics of Lyapunov exponents. Some definitions and propositions are given. The main intent is to use the 2D and 3D projections of the 5D trajectories on different subspaces, to construct the graphs of solutions for understanding and managing the system. Visualizations where possible, are provided.