Deterministic Chaos in One-Dimensional Continuous Systems.
Deterministic Chaos in One-Dimensional Continuous Systems
Jan Awrejcewicz, Vadim A. Krysko, Irina V. Papkova, and Anton V. Krysko
World Scientific Series on Nonlinear Science, Series A; Volume 90
After addressing the nonlinear dynamics of structural members, the graduate text presents novel methods for studying nonlinear phenomena exhibited by continuous systems with the help of Lyapunov exponents, wavelet-based analysis, and neural networks to achieve reliable results faster than classical approaches. The methodology relies on truncation of nonlinear partial differential equations governing the dynamics of structural members in a way that gives an approximated set containing a large number of nonlinear ordinary differential equations modelling real objects with infinite degrees of freedom. The opening chapters review the bifurcational and chaotic dynamics of structural members and necessary differential equations. ([umlaut] Ringgold, Inc., Portland, OR)