An efficient and stable approach for computation of Lyapunov characteristic exponents of continuous dynamical systems

Chaotic roll motions of ships in regular longitudinal waves

“…There are many algorithms that can calculate LCEs (Wolf et al, 1985;Rangarajan et al, 1998;Udwadia and Bremen, 2001), in this paper, a simple and high-efficiency algorithm is presented here to calculate Lyapunov characteristic exponents. In this method, QR -factorization is the fundamental solution of the system.…”

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

“…Let z − * be the one-periodic fixed point of the reduced controlled hybrid Poincaré map (21). Determination of this fixed point using expressions (21)- (22) is realized according to the previous section. Moreover, let K = [KǨ], whereK is a scalar.…”

“…Based on relations in (22), the controlled hybrid Poincaré map under the OGY control law (23) can be recast as:…”

Implementation of approach to compute the Lyapunov characteristic exponents for continuous dynamical systems to higher dimensions

“…LCEs provide a way to characterize the asymptotic behavior of nonlinear dynamical 10.020 systems by measuring the mean exponential growth (or shrinking) of perturbations with respect to a nominal trajectory. LCEs allow to measure the sensitivity of a dynamical system to small changes in initial conditions.…”

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A general method for accurately computing the Lyapunov characteristic exponents (LCEs) of continuous dynamical systems has been developed in [10]. In this paper, this method is extended to implementations on systems of arbitrary dimensions.

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