Modeling by nonlinear differential equations : dissipative and conservative processes / Paul E. Phillipson, Peter Schuster.

Includes bibliographical references (pages 213-222) and index.

1. Theme and contents of this book -- 2. Processes in closed and open systems. 2.1. Introduction. 2.2. Thermodynamics of general systems. 2.3. Chemical reactions. 2.4. Autocatalysis in closed and open systems -- 3. Dynamics of molecular evolution. 3.1. Introduction. 3.2. Selection and evolution. 3.3. Template induced autocatalysis. 3.4. Replicator equations. 3.5. Unlimited growth and selection -- 4. Relaxation oscillations. 4.1. Introduction. 4.2. Self-exciting relaxation oscillations. 4.3. Current induced neuron oscillations. 4.4. Bistability and complex structure of harmonically forced relaxation oscillations -- 5. Order and chaos. 5.1. Introduction. 5.2. One dimensional maps. 5.3. Lorenz equations. 5.4. Low dimensional autocatalytic networks. 5.5. Chua equations -- 6. Reaction diffusion dynamics. 6.1. Introduction. 6.2. Pulse front solutions of Fisher and related equations. 6.3. Diffusion driven spatial inhomogeneities. 6.4. Turing mechanism of chemical pattern formation -- 7. Solitons. 7.1. Introduction. 7.2. One dimensional lattice dynamics. 7.3. Burgers equation -- 8. Neuron pulse propagation. 8.1. Introduction. 8.2. Properties of a neural pulse. 8.3. FitzHugh-Nagumo equations. 8.4. Hodgkin-Huxley equations. 8.5. An overview -- 9. Time reversal, dissipation and conservation. 9.1. Introduction. 9.2. Irreversibility and diffusion. 9.3. Reversibility and time recurrence. 9.4. Complex dynamics and chaos in Newtonian dynamics : Hénon-Heiles equations.

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.

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