Coexistence and ergodicity in a variant Nose-Hoover oscillator and its FPGA implementation

As a classical volume-conservative system, the Nose-Hoover oscillator can generate conservative chaos and nested invariant tori. In this paper, a new 3D system is derived from the Nose-Hoover oscillator in which the coexisting phenomenon of conservative flow and dissipative attractor is discovered. We first numerically analyze the equilibrium points and their stabilities, and study the fold-Hopf bifurcation at the critical point. Then, the dynamic behaviors of the system are studied, besides the coexisting phenomenon, the system also has transient chaos. More interestingly, we find that the increase of parameter has a significant effect on enhancing the ergodicity of the system, which is also proved by the cross section with no "holes". Furthermore, we design a pseudo-random number generator based on the new system. Numerical results show that this PRNG can generate pseudo-random sequences with high randomness and is suitable for image encryption. Finally, we implement the system using FPGA technology.