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MODELING BY NONLINEAR DIFFERENTIAL EQUATIONS: DISSIPATIVE AND CONSERVATIVE PROCESSES
Author(s): Paul Phillipson (Author), Peter Schuster (Author)
- Publisher: World Scientific Publishing Company
- Publication Date: October 1, 2009
- Edition: Illustrated
- Language: English
- Print length: 240 pages
- ISBN-10: 9814271594
- ISBN-13: 9789814271592
Book Description
This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions
Editorial Reviews
Review
This is a quite unique book combining interesting models from key application areas which have been of long-standing interest in science and the mathematical tools for their qualitative analysis. –Heinz W Engl, Austrian Academy of Sciences
From the Back Cover
This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are nonlinear oscillations, deterministic chaos, solitons, reactiondiffusion-driven chemical pattern formation, neuron dynamics, autocatalysis and molecular evolution. Included is a discussion of processes from the vantage of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions.
