A numerical method for the computation of the Lyapunov exponents of nonlinear ordinary differential equations

Authors:
F. Carbonell;J. C. Jimenez;R. Biscay
Affiliations:
Departmento de Matematica Aplicada, Centro de Neurociencias de Cuba, Apartado 6880, La Habana, Cuba;Instituto de Cibernetica, Matematica y Fisica, Calle 15, el C y D, Vedado, La Habana 4, C.P. 10400, Cuba;Departamento de Matematica Aplicada, Facultad de Matematica y Computacion, Universidad de la Habana, San Lazaro y L, La Habana, C.P. 10400, Cuba
Venue:
Applied Mathematics and Computation
Year:
2002

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Abstract

In this paper, an alternative method to compute the Lyapunov exponents of dynamical systems described by ordinary differential equations (ODEs) is introduced. The Lyapunov exponents are computed in terms of the solutions of two piecewise linear ODEs that approximate, respectively, the solutions of the original ODE and its associated variational equation. This approach is strongly connected with the local linearization (LL) method for ODEs and its major advantage is that these piecewise linear ODEs might be exactly integrated in a non-simultaneous way. The performance of the method is illustrated with a numerical example.