Author | Vasiliev, V. A. author |
---|---|
Title | Autowave Processes in Kinetic Systems [electronic resource] : Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine / by V. A. Vasiliev, Yu. M. Romanovskii, D. S. Chernavskii, V. G. Yakhno |
Imprint | Dordrecht : Springer Netherlands, 1987 |
Connect to | http://dx.doi.org/10.1007/978-94-009-3751-2 |
Descript | VI, 262 p. online resource |
1 Autowave processes and their role in natural sciences -- 1.1 Autowaves in non-equilibrium 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 telegrapherโs equations -- 2.2 Nonlinear diffusion equation. Finite diffusion velocity -- 2.3 Diffusion in multicomponent homogeneous systems -- 2.4 Integro-differential 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 Small-parameter method -- 3.5 Axiomatic approach -- 3.6 Discrete models -- 3.7 Fast and slow phases of space-time processes -- 3.8 Group-theoretical 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 โslaveโ and โtriggerโ media -- 5.3 Stable leading centres -- 5.4 Standing waves -- 5.5 Reverberators: a qualitative description -- 6 Synchronization of auto-oscillations in space as a self-organization 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 auto-oscillators 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 quasi-harmonical 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 Self-organization 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 prey-predator system -- 8.4 Internal noise in distributed systems and spatial self-organization -- 8.5 External noise and dissipative structures โ linear theory -- 8.6 Nonlinear effects โ the two-box 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 blood-vessels with muscular walls -- 9.3 Autowave phenomena in plasmodia of Myxomycetes -- Concluding Remarks -- References