Lyapunov Exponents and Information Dimensions of Multi-Degree-of-Freedom Systems Under Deterministic and Stationary Random Excitations
The important concept of Lyapunov exponent has emerged in many fields in the last decade. It plays a crucial role in the determination of bifurcations and chaotic motions in nonlinear systems. Strategies for its numerical computation of multi-degree-of-freedom (MDOF) nonlinear systems under deterministic excitations are available in the literature [1–2]. For nonlinear systems under stochastic excitations, techniques available for the determination of Lyapunov exponents are very limited. They are confined to single degree-of-freedom (DOF) systems under stationary random excitations. For two DOF systems with small nonlinearities and under stationary random excitations of small intensities it is restricted to non-resonant cases. Essentially, these techniques have their basis on the work due to Khasminskii .
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