Chaotic dynamics of the Hunt model, an artificially constructed flow system with a hyperbolic attractor

TL;DR

This paper investigates the chaotic behavior of the Hunt model, a constructed continuous-time dynamical system with a hyperbolic attractor, providing visualizations, quantitative measures, and analysis of its chaotic dynamics.

Contribution

It offers the first detailed numerical analysis of the Hunt model's hyperbolic attractor, including visualizations, Lyapunov exponents, and symbolic dynamics, advancing understanding of such artificial chaotic systems.

Findings

Visualization of the hyperbolic attractor

Lyapunov exponents and attractor dimension estimates

Identification of unstable periodic orbits

Abstract

We study numerically chaotic behavior associated with a hyperbolic strange attractor of Plykin type in the model of Hunt, an artificially constructed dynamical system with continuous time. There are presented portraits of the attractor, plots of realizations for chaotic signal generated by the system, illustrations of the sensitive dependence on initial conditions for the trajectories on the attractor. Quantitative characteristics of the attractor are estimated, including the Lyapunov exponents and the attractor dimension. We discuss symbolic dynamics on the attractor, find out and analyze some unstable periodic orbit belonging to the attractor.