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Lyapunov Exponents and Information Dimensions of Multi-Degree-of-Freedom Systems Under Deterministic and Stationary Random Excitations

  • C. W. S. To
  • M. L. Liu
Part of the Solid Mechanics and its Applications book series (SMIA, volume 47)

Abstract

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 [3].

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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • C. W. S. To
    • 1
  • M. L. Liu
    • 2
  1. 1.Department of Mechanical EngineeringUniversity of Western OntarioLondonCanada
  2. 2.Department of Mechanical EngineeringLakehead UniversityThunder BayCanada

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