Ambrosio, Benjamin; Françoise, Jean-Pierre Propagation of bursting oscillations. (English) Zbl 1192.35009 Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1908, 4863-4875 (2009). Summary: We investigate a system of partial differential equations of reaction-diffusion type which displays propagation of bursting oscillations. This system represents the time evolution of an assembly of cells constituted by a small nucleus of bursting cells near the origin immersed in the middle of excitable cells. We show that this system displays a global attractor in an appropriated functional space. Numerical simulations show the existence in this attractor of recurrent solutions which are waves propagating from the central source. The propagation seems possible if the excitability of the neighbouring cells is above some threshold. Cited in 6 Documents MSC: 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 92C17 Cell movement (chemotaxis, etc.) Keywords:attractors; bursting; oscillations; excitable media; reaction diffusion PDFBibTeX XMLCite \textit{B. Ambrosio} and \textit{J.-P. Françoise}, Philos. Trans. R. Soc. Lond., Ser. A, Math. Phys. Eng. Sci. 367, No. 1908, 4863--4875 (2009; Zbl 1192.35009) Full Text: DOI References: [1] Aslanidi, Biophysical Journal 80 (3) pp 1195– (2001) · doi:10.1016/S0006-3495(01)76096-1 [2] Chialvo, Nature; Physical Science (London) 330 (6150) pp 749– (1987) · doi:10.1038/330749a0 [3] SIAM J APPL MATH 20 pp 816– (1989) · Zbl 0684.35055 · doi:10.1137/0520057 [4] Michaels, Circulation Research 65 (5) pp 1350– (1989) · doi:10.1161/01.RES.65.5.1350 [5] Physica. D 32 pp 327– (1988) · Zbl 0656.76018 · doi:10.1016/0167-2789(88)90062-0 [6] PHYS REV E 71 pp 036226– (2005) · doi:10.1103/PhysRevE.71.036226 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.