Comparison of Different Methods for Computing Lyapunov Exponents

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Abstract
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.