Chaotic Dynamics in a Sine Square Map: High-Dimensional Case (N≥3)

We study an N-dimensional system based on a sine square map and analyze the system behaviors of cases of dimension N≥3 with the tools of nonlinear dynamics. In the three-dimensional case, bifurcations in the parameter plane, invariant manifolds, critical manifolds and chaotic attractors are studied. Then we extend this study to the cases of higher dimension (N>3) to understand generalized properties of the system. The analysis and experimental results of the system demonstrate the existence of bounded chaotic orbits, which can be considered for secure transmissions.