Geodesic
Model of a spatially inhomogeneous one-dimensional active medium
Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 506-519

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We investigate the dynamics of one-dimensional discrete models of a one-component active medium analytically. The models represent spatially inhomogeneous diffusively concatenated systems of one-dimensional piecewise-continuous maps. The discontinuities (the defects) are interpreted as the differences in the parameters of the maps constituting the model. Two classes of defects are considered: spatially periodic defects and localized defects. The area of regular dynamics in the space of the parameters is estimated analytically. For the model with a periodic inhomogeneity, an exact analytic partition into domains with regular and with chaotic types of behavior is found. Numerical results are obtained for the model with a single defect. The possibility of the occurrence of each behavior type for the system as a whole is investigated. 
@article{TMF_2000_124_3_a10,
     author = {K. A. Vasil'ev and A. Yu. Loskutov and S. D. Rybalko and D. N. Udin},
     title = {Model of a spatially inhomogeneous one-dimensional active medium},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {506--519},
     publisher = {mathdoc},
     volume = {124},
     number = {3},
     year = {2000},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a10/}
}
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K. A. Vasil'ev; A. Yu. Loskutov; S. D. Rybalko; D. N. Udin. Model of a spatially inhomogeneous one-dimensional active medium. Teoretičeskaâ i matematičeskaâ fizika, Tome 124 (2000) no. 3, pp. 506-519. http://geodesic.mathdoc.fr/item/TMF_2000_124_3_a10/