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| Localized traveling wave is the main careers of information and the effect of heterogeneity in the media is of great importance for the understanding of signaling processes in biological and physiological systems. The role of heterogeneity in the media does not remain a perturbative effect, in fact it is well-known that it causes propagation failure such as pinning-depinning, and annihilation. There is, however, another aspect of heterogeneity-induced dynamics, namely it creates a spontaneous generator of pulses without any triggers and external forces. We try to clarify the underlying mechanism for such pulse generators from dynamical system viewpoint. Secondly, we discuss 2D spot dynamics in heterogeneous media. The simplest case is a jump-discontinuity along the line. Unlike the refraction of light, the Snell's law does not hold for dissipative traveling spots, but slightly different formula holds. We also discuss about the difference between monotone tail case and oscillatory tail case. |
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