Autowave Processes in Kinetic Systems : Spatial and Temporal SelfOrganization in Physics, Chemistry, Biology, and Medicine
 Responsibility
 by V.A. Vasiliev, Yu. M. Romanovskii, D.S. Chernavskii, V.G. Yakhno.
 Language
 English. English.
 Digital
 text file
 Imprint
 Dordrecht : Springer Netherlands, 1987.
 Physical description
 1 online resource (264 pages)
 Series
 Mathematics and Its Applications, Soviet Series, ; 11.
Online
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Description
Creators/Contributors
 Author/Creator
 Vasilʹev, V. A. (Vladislav Andreevich)
 Contributor
 Romanovskii, Yu. M.
 Chernavskii, D. S.
 I͡Akhno, V. G. (Valeriĭ Georgievich)
Contents/Summary
 Contents

 1 Autowave processes and their role in natural sciences
 1.1 Autowaves in nonequilibrium systems
 1.2 Mathematical model of an autowave system
 1.3 Classification of autowave processes
 1.4 Basic experimental data
 2 Physical premises for the construction of basic models
 2.1 Finite interaction velocity. Reduction of telegrapher's equations
 2.2 Nonlinear diffusion equation. Finite diffusion velocity
 2.3 Diffusion in multicomponent homogeneous systems
 2.4 Integrodifferential equations and their reduction to the basic model
 2.5 Anisotropic and dispersive media
 2.6 Examples of basic models for autowave systems
 3 Ways of investigation of autowave systems
 3.1 Basic stages of investigation
 3.2 A typical qualitative analysis of stationary solutions in the phase plane
 3.3 Study of the stability of stationary solutions
 3.4 Smallparameter method
 3.5 Axiomatic approach
 3.6 Discrete models
 3.7 Fast and slow phases of spacetime processes
 3.8 Grouptheoretical approach
 3.9 Numerical experiment
 4 Fronts and pulses: elementary autowave structures
 4.1 A stationary excitation front
 4.2 A typical transient process
 4.3 Front velocity pulsations
 4.4 Stationary pulses
 4.5 The formation of travelling pulses
 4.6 Propagation of pulses in a medium with smooth inhomogeneities
 4.7 Pulses in a medium with a nonmonotonic dependence v = v(y)
 4.8 Pulses in a trigger system
 4.9 Discussion
 5 Autonomous wave sources
 5.1 Sources of echo and fissioning front types
 5.2 Generation of a TP at a border between 'slave' and 'trigger' media
 5.3 Stable leading centres
 5.4 Standing waves
 5.5 Reverberators: a qualitative description
 6 Synchronization of autooscillations in space as a selforganization factor
 6.1 Synchronization in homogeneous systems
 6.2 Synchronization in inhomogeneous systems. Equidistant detuning case
 6.3 Complex autowave regimes arising when synchronization is violated
 6.4 A synchronous network of autooscillators in modern radio electronics
 7 Spatially inhomogeneous stationary states: dissipative structures
 7.1 Conditions of existence of stationary inhomogeneous solutions
 7.2 Bifurcation of solutions and quasiharmonical structures
 7.3 Multitude of structures and their stability
 7.4 Contrast dissipative structures
 7.5 Dissipative structures in systems with mutual diffusion
 7.6 Localized dissipative structures
 7.7 Selforganization in combustion processes
 8 Noise and autowave processes
 8.1 Sources of noise in active kinetic systems and fundamental stochastic processes
 8.2 Parametric and multiplicative fluctuations in local kinetic systems
 8.3 The mean life time of the simplest ecological preypredator system
 8.4 Internal noise in distributed systems and spatial selforganization
 8.5 External noise and dissipative structures
 linear theory
 8.6 Nonlinear effects
 the twobox model
 8.7 Wave propagation and phase transitions in media with distributed multiplicative noise
 9 Autowave mechanisms of transport in living tubes
 9.1 Autowaves in organs of the gastrointestinal tract
 9.2 Waves in small bloodvessels with muscular walls
 9.3 Autowave phenomena in plasmodia of Myxomycetes
 Concluding Remarks
 References.
 Summary
 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. JoliotCurie 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 oxidationreduction 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)
Subjects
Bibliographic information
 Publication date
 1987
 Series
 Mathematics and Its Applications, Soviet Series, 01696378 ; 11
 ISBN
 9789400937512 (electronic bk.)
 9400937512 (electronic bk.)
 9789401081726 (print)
 9401081727 (print)
 DOI
 10.1007/9789400937512