By V.A. Vasiliev, Yu.M. Romanovskii, D.S. Chernavskii, V.G. Yakhno

Probably, we're obliged to technology, greater than to the other box of the human job, for the foundation of our feel that collective efforts are helpful certainly. F. Joliot-Curie The research of autowave approaches is a tender technological know-how. Its uncomplicated suggestions and strategies are nonetheless within the strategy of formation, and the sphere of its purposes to varied domain names of average sciences is increasing consistently. incredible examples of varied autowave procedures are saw experimentally in different laboratories of relatively diversified orientations, facing investigations in physics, chemistry and biology. it's O1). r opinion, although, that if a heritage of the invention of autowaves will he written a few day its writer may still without doubt point out 3 primary phenomena that have been the resources of the area in view. "Ve suggest combustion and section transition waves, waves in chemical reactors the place oxidation-reduction approaches ensue, and propagation of excitations in nerve fibres. the most instruments of the speculation of autowave procedures are numerous equipment used for investigating nonlinear discrete or disbursed oscillating platforms, the mathe matical conception of nonlinear parabolic differential equations, and strategies of the speculation of finite automata. it truly is noteworthy that the speculation of autowave,. , has been enormously contributed to be paintings of awesome mathematicians who expected the experimental discoveries of their summary stories. One should still point out R. Fishel' (1937), A. N. Kolmogorov, G. 1. Petrovskii, and N. S. Piskunov (1937), N. Wiener and A. Rosenbluth (1946), A. Turing (1952).

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**Additional info for Autowave Processes in Kinetic Systems: Spatial and Temporal Self-Organization in Physics, Chemistry, Biology, and Medicine**

**Sample text**

Because of these functions, the local system has a stable circular limit cycle. Iterative methods based upon the Floquet theory are appropriate for analysis of AWPs in A-W systems, as the exact zero (homogeneous) approximation is always known. These methods were used to show the variety of AWPs in reactive systems with diffusion (Ortoleva and Ross 1974); one- and two-dimensional waves, and in particular rotating waves (reverberators) were detected. 7. The AWP theory was substantially contributed to by investigations of the models for the Belousov-Zhabotinskii distributed chemical reaction.

For example, for n = 2 and in the absence of an external field one has v+c+z+ v_c_z_ = 0, so that v+ = v_, or 1+ = L, and the number of independent moving components is reduced by one. In general, the number of independent fluxes is the sum of the molecule and ion types minus the number of reactions of the local chemical equilibrium, and minus one. 'Therefore for a single substance dissociating into two ions with the dissociation constant cx, one has a single independent flux, 12 = -D grad C2 , 1+ = v+cxl2 and L = v_cxl2 (v+, v_ are the ion decay coefficients).

2 2 Physical premises for the construction of basic models Nonlinear diffusion equation. 3) can be used also for the description of mass and heat transport with a finite velocity, even in the absence of sources (F(x) = 0), if the diffusion coefficient depends on the variable x, vanishing at some value (Zeldovich and Kompaneets 1950, Barenblatt 1952, Barenblatt and Vishik 1956). We are going to elucidate this point with an example and then to discuss briefly some media with such a dependence of D on x.