Nonlinear Dynamics
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Nonlinear Dynamics and Chaos
This textbook is aimed at newcomers to nonlinear dynamics and chaos, especially students taking a first course in the subject. The presentation stresses analytical methods, concrete examples, and geometric intuition. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.
Nonlinear Dynamics and Statistics
Author: Alistair I. Mees
language: en
Publisher: Springer Science & Business Media
Release Date: 2001-01-25
This book describes the state of the art in nonlinear dynamical reconstruction theory. The chapters are based upon a workshop held at the Isaac Newton Institute, Cambridge University, UK, in late 1998. The book's chapters present theory and methods topics by leading researchers in applied and theoretical nonlinear dynamics, statistics, probability, and systems theory. Features and topics: * disentangling uncertainty and error: the predictability of nonlinear systems * achieving good nonlinear models * delay reconstructions: dynamics vs. statistics * introduction to Monte Carlo Methods for Bayesian Data Analysis * latest results in extracting dynamical behavior via Markov Models * data compression, dynamics and stationarity Professionals, researchers, and advanced graduates in nonlinear dynamics, probability, optimization, and systems theory will find the book a useful resource and guide to current developments in the subject.
Nonlinear Dynamics
Author: Muthusamy Lakshmanan
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
Integrability, chaos and patterns are three of the most important concepts in nonlinear dynamics. These are covered in this book from fundamentals to recent developments. The book presents a self-contained treatment of the subject to suit the needs of students, teachers and researchers in physics, mathematics, engineering and applied sciences who wish to gain a broad knowledge of nonlinear dynamics. It describes fundamental concepts, theoretical procedures, experimental and numerical techniques and technological applications of nonlinear dynamics. Numerous examples and problems are included to facilitate the understanding of the concepts and procedures described. In addition to 16 chapters of main material, the book contains 10 appendices which present in-depth mathematical formulations involved in the analysis of various nonlinear systems.