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2 results

  • 5 - Analysis of Discrete Dynamical Systems

  • from Part I - Matrix Methods
  • Kevin W. Cassel, Illinois Institute of Technology
  • Book:
    Matrix, Numerical, and Optimization Methods in Science and Engineering
    Published online:
    18 February 2021
    Print publication:
    04 March 2021, pp 253-312

  • Summary

    A dynamical system is a mechanical, electrical, chemical, or biological system that evolves in time.Dynamical systems theory provides one of the most powerful and pervasive applications of matrix methods in science and engineering.These qualitative and quantitative tools and methods allow for the determination and characterization of the number and types of solutions, including their stability, of complex, often nonlinear, systems.These methods include phase-plane analysis, bifurcation diagrams, stability theory, Poincare diagrams illustrated using linear and nonlinear physical examples, including the Duffing equation and the Saltzman-Lorenz model.

  • Non-linear threshold autoregressive models for non-linear random vibrations

  • Tohru Ozaki
  • Journal:
    Journal of Applied Probability / Volume 18 / Issue 2 / June 1981
    Published online by Cambridge University Press:
    14 July 2016, pp. 443-451
    Print publication:
    June 1981

  • Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models. Stationarity conditions and some structural aspects of the model are briefly discussed. Applications of the model in the statistical analysis of real data are also shown with numerical results.