Lyapunov exponents of a dynamical system give information about its long‐term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In this paper, an algorithm which optimizes Lyapunov exponents estimation in piecewise linear systems has been developed. The algorithm exploits the linearity of the state equation and of the variational equation to accurately evaluate Lyapunov exponents with a reduced execution time.
A fast algorithm for Lyapunov exponents calculation in piecewise linear systems
CANNAS, BARBARA;PISANO, FABIO
2011-01-01
Abstract
Lyapunov exponents of a dynamical system give information about its long‐term evolution. Exponents estimation is not an easy task; it is computationally costly and, in presence of chaotic dynamics, it exhibits numerical difficulties. In this paper, an algorithm which optimizes Lyapunov exponents estimation in piecewise linear systems has been developed. The algorithm exploits the linearity of the state equation and of the variational equation to accurately evaluate Lyapunov exponents with a reduced execution time.
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