From geodesic flow on a surface of negative curvature to electronic generator of robust chaos

TL;DR

This paper introduces an electronic circuit that generates robust chaos by emulating the hyperbolic chaotic dynamics of geodesic flow on a negatively curved surface, supported by simulations and numerical analysis.

Contribution

It presents a novel electronic circuit design that replicates hyperbolic chaos, bridging geometric dynamical systems and practical chaos generators.

Findings

Circuit simulation confirms chaotic behavior matching theoretical models.

Lyapunov exponents indicate strong chaos.

Fourier spectra show broad frequency content.

Abstract

Departing from the geodesic flow on a surface of negative curvature as a classic example of the hyperbolic chaotic dynamics, we propose an electronic circuit operating as a generator of rough chaos. Circuit simulation in NI Multisim software package and numerical integration of the model equations are provided. Results of computations (phase trajectories, time dependences of variables, Lyapunov exponents and Fourier spectra) show good correspondence between the chaotic dynamics on the attractor of the proposed system and of the Anosov dynamics for the original geodesic flow.