Patterns and Dynamics in Reactive Media by Claude Baesens, John Guckenheimer, Seunghwan Kim (auth.),

By Claude Baesens, John Guckenheimer, Seunghwan Kim (auth.), Rutherford Aris, Donald G. Aronson, Harry L. Swinney (eds.)

Ever because the seminal works on touring waves and morphogenesis by way of Fisher, via Kolmogorov, Petrovski and Piscunov, and through Turing, scientists from many disciplines were serious about questions about the formation of regular or dynamic styles in reactive media. Contributions to this quantity were made through chemists, chemical engineers, mathematicians (both natural and applied), and physicists. the subjects lined diversity from studies of experimental stories, via descriptions of numerical experiments, to particularly summary theoretical investigations, each one displaying varied features of a really various field.

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1. 1. 7 49 It will be instructive to consider another example.

J) > 0 for any spacing in the train, still leaves us with many solutions. We therefore conclude that a multitude of stable wavetrains, mostly nonuniform, can exist in the case of oscillatory recovery. As the number of impulses, N, becomes large the systems develops extreme sensitivity to initial conditions and to external noise. 5) rather easily. Setting Xj = canst. 5) we find a pattern map which relates a given spacing to the successive one [8,9). Periodic wavetrains and finite wavetrains correspond, respectively, to periodic and homoclinic orbits of that map.

Rev. A, 40 (1989), pp. 3226-3230 [8] C. Elphick, E. Meron and E. A. Spiegel, Patterns of propagating pulses, to appear in SIAM J. App!. Math .. [9] C. Elphick, E. Meron and E. A. Spiegel, Spatiotemporal complexity in traveling patterns, Phys. Rev. , 61 (1988), pp. 496-499. [10] The manner by which a rectilinear wavefront with a free end evolves toward a rotating spiral wave has been studied in E. Meron and P. Pelce, Model for spiral wave formation in excitable media, Phys. Rev. , 60 (1988), pp.

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