1990/05/01 by K. Geist, Karlheinz Geist, U. Parlitz +3 · 6 citations
Computer Science · Physics and Astronomy · #Chaos control and synchronization #Nonlinear Dynamics and Pattern Formation #Quantum chaos and dynamical systems
paper · pdf · doi:10.1143/ptp.83.875
crossref issued 1990/05/01 · crossref published 1990/05/01 · crossref published-print 1990/05/01 · openalex publication_date 1990/05/01 · crossref created 2005/12/14 · crossref deposited 2019/04/10 · openalex created_date 2025/10/10 · crossref indexed 2026/07/30 · openalex updated_date 2026/07/31
Different discrete and continuous methods for computing the Lyapunov exponents of dynamical systems are compared for their efficiency and accuracy. All methods are either based on the QR or the singular value decomposition. The relationship between the discrete methods is discussed in terms of the iteration algorithms and the decomposition procedures used. We give simple derivations of the differential equations for continuous methods proposed recently and show that they cannot be recommended because of their long computation time and numerical instabilities. The methods are tested with the damped and driven Toda chain and the driven van der Pol oscillator.