A dynamical system with a strange attractor and invariant tori

• Published in: Physics letters. A Vol. 378; no. 20; pp. 1361 - 1363
• Main Author: Sprott, J.C.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 04-04-2014
• Subjects: Dissipation; Dynamical system; Dynamical systems; Initial conditions; Invariant torus; Invariants; Orbits; Solid state physics; Strange attractor; Strange attractors; Three dimensional; Strange attractor; Invariant torus; Dynamical system
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2014.03.028

This paper describes a simple three-dimensional time-reversible system of ODEs with quadratic nonlinearities and the unusual property that it is exhibits conservative behavior for some initial conditions and dissipative behavior for others. The conservative regime has quasi-periodic orbits whose amplitude depend on the initial conditions, while the dissipative regime is chaotic. Thus a strange attractor coexists with an infinite set of nested invariant tori in the state space.
•A new three-dimensional quadratic ODE system is described.•The system is bounded, chaotic, and has no equilibrium points.•A strange attractor coexists with nested invariant tori.•The strange attractor has a symmetric twin strange repellor.•The strange attractor is hidden because there are no equilibria.