Proof of The Rossler-Hala Digital Switch Operation

This letter defines the Rossler-Hala Digital Switch, a novel framework for the deterministic control of chaotic manifolds through the mechanism of successive controlled collapse. By manipulating the feedback parameter γ, we demonstrate a functional mapping between the continuous 3D R¨ossler-Hala attractor and the discrete 1D logistic map. The ”switch” operates by utilizing active perturbations to quench the system’s strange attractor into stable fixed points, effectively digitizing a chaotic signal into discrete logical states. We analyze the volumetric contraction of the basin of attraction and the resulting Lyapunov spectrum to prove that the system can be forced into periodic windows or quiescent states with high precision. This architecture provides a robust foundation for secure communications and the regulation of complex plasma systems.