Overview

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

Full Product Details

Author:   Paul Phillipson (Univ Of Colorado Boulder, Usa) ,  Peter Schuster (Univ Wien, Austria)
Publisher:   World Scientific Publishing Co Pte Ltd
Imprint:   World Scientific Publishing Co Pte Ltd
Volume:   69
Dimensions:   Width: 16.50cm , Height: 1.50cm , Length: 24.90cm
Weight:   0.590kg
ISBN:  

9789814271592

ISBN 10:   9814271594
Pages:   240
Publication Date:   01 October 2009
Audience:   College/higher education ,  Professional and scholarly ,  Tertiary & Higher Education ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   Awaiting stock  
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Table of Contents

Relaxation Oscillations: Self-Exciting Oscillations Displayed by the van der Pol and Stoker-Haag Equations; Current-Induced Neuron Oscillations; Bistability and Complex Oscillations of Harmonically Forced Relaxation Oscillations; Order and Chaos: Predictions by the Lorentz Equations; Chua Equations and Autocatalytic Networks; Encapsulation of Bifurcation Sequences by Specifically Constructed One-Dimensional Maps; Reaction-Diffusion Dynamics: Pulse-Front Solutions to the Fisher and Related Equations; Diffusion-Driven Spatial Limit Cycles; Turing Mechanism of Chemical Pattern Formation; Solitons: Lattice Dynamics and the Korteweg-deVries Equation; Sine-Gordon Equation; Burgers' Equation; Neuron Pulse Propagation: FitzHugh-Nagumo Equations and Hodgkin-Huxley Equations; Dynamics of Self-Replication and Evolution: Autocatalysis; Selection; Symbiosis and Cooperation; Time Reversal, Dissipation and Conservation: Linear Diffusion as a Stochastic Process: Random Walks; Langevin's Equation; Diffusion as Asymptotic Realization of Newtonian Dynamics; Recurrence Times; Nonlinear Fermi-Pasta-Ulam Model and the Toda Lattice.

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