Mathematical Models Of Chemical Reactions: Theory And Applications Of Deterministic And Stochastic Models

NONLINEAR SCIENCE THEORY AND APPLICATIONS Numerical experiments over the last thirty years have revealed that simple nonlinear systems can have surprising and complicated behaviours. Nonlinear phenomena include waves that behave as particles, deterministic equations having irregular, unpredictable solutions, and the formation of spatial structures from an isotropic medium. The applied mathematics of nonlinear phenomena has provided metaphors and models for a variety of physical processes: solitons have been described in biological macromolecules as well as in hydrodynamic systems; irregular activity that has been identified with chaos has been observed in continuously stirred chemical flow reactors as well as in convecting fluids: nonlinear reaction diffusion systems have been used to account for the formation of spatial patterns in homogeneous chemical systems as well as biological morphogenesis; and discrete-time and discrete-space nonlinear systems (cellular automata) provide metaphors for processes ranging from the microworld of particle physics to patterned activity in computing neural and self-replicating genetic systems. Nonlinear Science: Theory and Applications will deal with all areas of nonlinear science - its mathematics, methods and applications in the biological, chemical, engineering and physical sciences. Nonlinear science: theory and applications Series editor: Arun V. Holden, Reader in General Physiology, Centre for Nonlinear Studies, The University, Leeds LS2 9NQ, UK Editors: S. I. Amari (Tokyo), P. L. Christiansen (Lyngby), D. G. Crighton (Cambridge), R. H. G. Heileman (Houston), D. Rand (Warwick), J. C. Roux (Bordeaux) Chaos A. V. Holden (Editor) Control and optimization J. E. Rubio Automata networks in computer science F. Fogelman Soulie, Y. Robert and M. Tchuente (Editors) Oscillatory evolution processes I. Gumowski Introduction to the theory of algebraic invariants of differential equations K. S. Sibirsky Simulation of wave processes in excitable media V. Zykov (Edited by A. T. Winfree and P. Nandapurkar) Almost periodic operators and related nonlinear integrable systems V. A. Chulaevsky Other volumes are in preparation Mathematical models of '· chemical reaction~_/ Theory and applications of deterministic and stochastic models P. Erdi and J. T6th Central Research Institute for Physics, Hungarian Academy of Sciences and Computer and Automation Institute, Hungarian Academy of Sciences c Manchester University Press Copyright© P. Erdi and J. Toth 1989 Published by Manchester University Press Oxford Road, Manchester MI3 9PL, UK British Library cataloguing in publication data Erdi, P. Mathematical models of chemical reactions: theory and applications of deterministic and stochastic models.- (Nonlinear science) I. Chemical reactions - Mathematical models I. Title II. Toth, J. III. Series 541.3'9'0724 QD501 ISBN 0 7190 2208 8 hardback Typeset in Times 10/12 pt by Graphicraft Typesetters Ltd, Hong Kong Printed in Great Britain by Biddies Ltd., Guildford and King's Lynn Contents Preface and acknowledgements Symbols used in the text XI xm 1 Chemical kinetics: a prototype of nonlinear science 1.1 Mass action kinetics: macroscopic and microscopic approach 1.2 Physical models of chemical reactions 1.3 Deterministic and stochastic models 1.4 Regular and exotic behaviour 1.5 Chemical kinetics as a metalanguage I 4 6 II 12 2 The structure of kinetic models 2.1 Temporal processes 2.2 Properties of process-time 2.2.1 Discrete versus continuous 2.2.2 Time, thermodynamics, chemical kinetics 2.3 Structure of state-space 2.3.1 Discrete versus continuous 2.3.2 State and site 2.4 Nature of determination 2.5 X YZ models 14 14 14 15 15 16 16 17 18 19 3 Stoichiometry: the algebraic structure of complex chemical reac