Smooth and Nonsmooth High Dimensional Chaos and the Melnikov-Type Methods (World Scientific Nonlinear Science Series a) by Jan Awrejcewicz (PDF)

Description

This book focuses on the development of Melnikov-type methods applied to high dimensional dynamical systems governed by ordinary differential equations. Although the classical Melnikov’s technique has found various applications in predicting homoclinic intersections, it is devoted only to the analysis of three-dimensional systems (in the case of mechanics, they represent one-degree-of-freedom nonautonomous systems). This book extends the classical Melnikov’s approach to the study of high dimensional dynamical systems, and uses simple models of dry friction to analytically predict the occurrence of both stick-slip and slip-slip chaotic orbits, research which is very rarely reported in the existing literature even on one-degree-of-freedom nonautonomous dynamics.This pioneering attempt to predict the occurrence of deterministic chaos of nonlinear dynamical systems will attract many researchers including applied mathematicians, physicists, as well as practicing engineers. Analytical formulas are explicitly formulated step-by-step, even attracting potential readers without a rigorous mathematical background.

User’s Reviews

Editorial Reviews: Review This book is intended for scientists and engineers interested in predicting the chaotic behaviour of their models of interest, as well as for graduate students attending courses in applied dynamical systems. –Mathematical Reviews

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