Proof of the Sprott A-Hala Clock Operation

This letter introduces the Sprott A-Hala Clock, a deterministic frequency oscillator engineered by suppressing chaos within a non-equilibrium hidden attractor. Unlike conventional oscillators that depend on stable linear resonators, this system leverages the unique topological properties of the Sprott A system, which inherently lacks equilibrium points. By applying a controlled feedback parameter, γ, we demonstrate a “Successive Controlled Collapse” wherein a three-dimensional chaotic manifold is forced onto a one-dimensional periodic limit cycle. We establish a mathematical isomorphism between the feedback intensity and the bifurcation structure of the system, allowing for the precise selection of stable periodic windows. The resulting oscillator exhibits high temporal stability, offering significant potential for applications in plasma physics, gaseous electronics, and the development of robust “Digital Switch” timing architectures in high-noise environments.