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Nonlinear Dynamics and Stochastic Mechanics
Edited by: Wolfgang H. Kliemann, Iowa State University, Ames, IA, William F. Langford, University of Guelph, ON, Canada, and N. S. Namachchivaya, University of Illinois, Urbana-Champaign, IL
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
1996; 238 pp; hardcover
Volume: 9
ISBN-10: 0-8218-0257-7
ISBN-13: 978-0-8218-0257-1
List Price: US$90
Member Price: US$72
Order Code: FIC/9
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This volume contains the proceedings of the International Symposium on Nonlinear Dynamics and Stochastic Mechanics held at The Fields Institute for Research in Mathematical Sciences from August-September (1993) as part of the 1992-1993 Program Year on Dynamical Systems and Bifurcation Theory.

In recent years, mathematicians and applied scientists have made significant progress in understanding and have developed powerful tools for the analysis of the complex behavior of deterministic and stochastic dynamical systems. By moving beyond classical perturbation methods to more general geometrical, computational, and analytical methods, this book is at the forefront in transferring these new mathematical ideas into engineering practice.

This work presents the solutions of some specific problems in engineering structures and mechanics and demonstrates by explicit example these new methods of solution.


  • Joins problems in engineering science to recent developments in the mathematical theory of dynamical systems.
  • Offers novel applications of dynamical systems theory.
  • Presents numerical methods for stochastic systems.
  • Compares analytical and numerical studies near the onset of chaos.
  • In one volume, brings together and contrasts deterministic and stochastic models of "chaos".

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students, applied mathematicians, and engineers working in nonlinear chaotic and stochastic behavior of mechanical systems and structures.

Table of Contents

  • B. Banerjee and A. K. Bajaj -- Chaotic responses in two degree-of-freedom systems with 1:2 internal resonances
  • L. A. Bergman, B. F. Spencer, S. F. Wojtkiewicz, and E. A. Johnson -- Robust numerical solution of the Fokker-Planck equation for second order dynamical systems under parametric and external white noise excitations
  • C. Bucher -- Stochastic stability of systems with random properties
  • S. H. Crandall -- Oil whirl and oil whip, nonlinear limit-cycle phenomena
  • E. H. Dowell and A. L. Katz -- A basic explanation of homoclinic intersection in the twin-well duffing oscillator
  • N. Hofmann and E. Platen -- Stability of superimplicit numerical methods for stochastic differential equations
  • R. A. Ibrahim and Y. J. Yoon -- Response statistics of nonlinear systems to parametric filtered white noise
  • R. Z. Khasminskii -- On robustness of some concepts in stability of stochastic differential equations
  • Y. W. Li, I. Elishakoff, J. H. Starnes, and M. Shinozuka -- Prediction of natural frequency and buckling load variability due to uncertainty in material properties by convex modeling
  • Y. Lin and G. Q. Cai -- Some results related to failure of stochastic structural systems
  • P. A. Meehan and S. F. Asokanthan -- Chaotic motion in a rotating body with internal energy dissipation
  • V. Wihstutz -- Numerics for Lyapunov exponents of hypoelliptic linear stochastic systems
  • W.-C. Xie and S. T. Ariaratnam -- Vibration mode localization in large randomly disordered continuous beams
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