DocumentCode
1832651
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
fYear
2008
fDate
18-21 May 2008
Firstpage
764
Lastpage
767
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;
fLanguage
English
Publisher
ieee
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
Type
conf
DOI
10.1109/ISCAS.2008.4541530
Filename
4541530
Link To Document