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PULSES, FRONTS AND CHAOTIC WAVE TRAINS IN A ONE-DIMENSIONAL CHUA’S LATTICE



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Papers International Journal of Bifurcation and Chaos Vol 7 No 8 1997 1775 1790 c World Scientific Publishing Company PULSES FRONTS AND CHAOTIC WAVE TRAINS IN A ONE DIMENSIONAL CHUA S LATTICE V B KAZANTSEV V I NEKORKIN The Nizhny Novgorod State University 23 Gagarin Ave 603600 Nizhny Novgorod Russia M G VELARDE Instituto Pluridisciplinar Universidad Complutense Paseo Juan XXIII N o 1 Madrid 28 040 Spain Received March 2 1997 Revised September 20 1997 We show how wave motions propagate in a nonequilibrium discrete medium modeled by a onedimensional array of diffusively coupled Chua s circuits The problem of the existence of the stationary wave solutions is reduced to the analysis of bounded trajectories of a fourth order system of nonlinear ODEs Then we study the homoclinic and heteroclinic bifurcations of the ODEs system The lattice can sustain the propagation of solitary pulses wave fronts and complex wave trains with periodic or chaotic profile 1 Introduction Many systems modeling processes in nonequilibrium excitable media are known to display solutions localized in space and steadily translating Solitary pulses fronts and wave trains propagating with a constant velocity are particular cases Examples come from all areas of science and engineering Take for instance waves in fluids Nepomnyashchy Velarde 1994 concentration waves in oscillatory reaction diffusion systems Zhabotinsky 1974 Kuramoto 1984 waves in optical fibers Hasegawa Kodama 1995 Huang Velarde 1996 pulses and pulse trains in long arrays of Josephson junctions Lonngren Scott 1995 transmission of excitation in neural fibers Murray 1993 etc Models allowing to describe such processes are appropriate Ginzburg Landau equations Van Saarloos Hohenberg 1992 the Korteweg de Vries equation Nekorkin Velarde 1994 Velarde et al 1995 Christov Velarde 1995 the model of Fitz Hugh Nagumo Murray 1993 and their generalizations Nepomnyashchy Velarde 1994 There has also been growing interest in models composed of coupled



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