Title :
Rigorous study of short periodic orbits for the Lorenz system
Author :
Galias, Zbigniew ; Tucker, Warwick
Author_Institution :
Dept. of Electr. Eng., AGH-Univ. of Sci. & Technol., Krakow
Abstract :
The existence of short periodic orbits for the Lorenz system is studied rigorously. We describe a method for finding all short cycles embedded in a chaotic singular attractor (i.e. an attractor containing an equilibrium). The method uses an interval operator for proving the existence of periodic orbits in regions where it can be evaluated, and bounds for the return time in other regions. The six shortest periodic orbits for the Lorenz system are found.
Keywords :
chaos; Lorenz system; chaotic singular attractor; short periodic orbits; Chaos; Continuous time systems; Differential equations; Jacobian matrices; Mathematics; Nonlinear dynamical systems; Orbits; Solid modeling; Testing; Trajectory;
Conference_Titel :
Circuits and Systems, 2008. ISCAS 2008. IEEE International Symposium on
Conference_Location :
Seattle, WA
Print_ISBN :
978-1-4244-1683-7
Electronic_ISBN :
978-1-4244-1684-4
DOI :
10.1109/ISCAS.2008.4541530
