A simple three-dimensional quadratic flow with an
attracting torus
Mahtab Mehrabbeika, Sajad Jafaria,b,∗,
Julien Clinton Sprottc aDepartment of Biomedical Engineering,
Amirkabir University of Technology (Tehran Polytechnic), Tehran,
Iran bHealth Technology Research Institute,
Amirkabir University of Technology (Tehran Polytechnic), Tehran,
Iran cDepartment of Physics, University of
Wisconsin, Madison, WI 53706, USA
Received 9 July 2022 Received in revised form 2 September 2022 Accepted 4 September 2022 Available online 13 September 2022 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.
Ref:
M. Mehrabbeik, S. Jafari, J. C. Sprott, Physics Letters A 451,
128427--1-8 (2022).