Two-Dimensional Rotation of Chaotic Attractors: Demonstrative Examples and FPGA Realization

In this work, we demonstrate the possibility of performing two-dimensional rotation on a chaotic system. This enables the rotation of its attractor in space without changing its chaotic dynamics. In particular, the rotated system preserves the same eigenvalues at all equilibrium points and its largest Lyapunov exponent remains unchanged. Two chaotic systems, one of which is the classical Lorenz system, are used to illustrate and validate the rotation operation using numerical simulations and further experimentally using a digital FPGA platform.