A simple three-dimensional quadratic flow with an attracting torus

Abstract

Attracting torus is a rare phenomenon in the dynamics of low-dimensional autonomous systems. Adding an anti-damping term to the well-known Nosé-Hoover oscillator, this paper introduces a new system exhibiting attracting torus in a wide range of parameter values. This system has a variety of dynamical solutions like limit cycles, strange attractors, attracting tori, invariant tori, and chaotic sea. It is also demonstrated that the system is multistable in some regions of parameter space wherein different types of attractors coexist. However, the attracting torus is the leading bounded solution in a considerable area of parameter space. Moreover, the coexistence of four limit cycles is found in the time-reversed system. The study of the system's basin of attraction shows that the system owns a solid basin of attraction with rounded boundaries for the attracting torus, which is an exciting property.