Modeling by nonlinear differential equations : dissipative and conservative processes
Author(s)
Bibliographic Information
Modeling by nonlinear differential equations : dissipative and conservative processes
（World Scientific series on nonlinear science / editor, Leon O. Chua, . series A ; v. 69）
World Scientific, c2009
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Note
Includes bibliographical references (p. 213-222) and index
Description and Table of Contents
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
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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