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Autowave Processes in Kinetic Systems

Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine

  • Authors
  • V. A. Vasiliev
  • Yu. M. Romanovskii
  • D. S. Chernavskii
  • V. G. Yakhno

Part of the Mathematics and Its Applications book series (MASS, volume 11)

Table of contents

  1. Front Matter
    Pages 1-10
  2. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 11-27
  3. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 28-51
  4. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 52-85
  5. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 86-114
  6. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 115-144
  7. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 145-163
  8. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 164-202
  9. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 203-224
  10. V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno
    Pages 225-242
  11. Back Matter
    Pages 243-262

About this book

Introduction

Probably, we are obliged to Science, more than to any other field of the human activity, for the origin of our sense that collective efforts are necessary indeed. F. Joliot-Curie The study of autowave processes is a young science. Its basic concepts and methods are still in the process of formation, and the field of its applications to various domains of natural sciences is expanding continuously. Spectacular examples of various autowave processes are observed experimentally in numerous laboratories of quite different orientations, dealing with investigations in physics, chemistry and biology. It is O1). r opinion, however, that if a history of the discovery of autowaves will he written some day its author should surely mention three fundamental phenomena which were the sources of the domain in view. "Ve mean combustion and phase transition waves, waves in chemical reactors where oxidation-reduction processes take place, and propagation of excitations in nerve fibres. The main tools of the theory of autowave processes are various methods used for investigating nonlinear discrete or distributed oscillating systems, the mathe­ matical theory of nonlinear parabolic differential equations, and methods of the theory of finite automata. It is noteworthy that the theory of autowave,. , has been greatly contributed to be work of brilliant mathematicians who anticipated the experimental discoveries in their abstract studies. One should mention R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).

Keywords

bifurcation biology differential equation stability

Bibliographic information

  • DOI https://doi.org/10.1007/978-94-009-3751-2
  • Copyright Information Springer Science+Business Media B.V. 1987
  • Publisher Name Springer, Dordrecht
  • eBook Packages Springer Book Archive
  • Print ISBN 978-94-010-8172-6
  • Online ISBN 978-94-009-3751-2
  • Series Print ISSN 0169-6378
  • Buy this book on publisher's site
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