Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2001-06-21
Nonlinear Sciences
Pattern Formation and Solitons
9 pages, 8 figures
Scientific paper
10.1103/PhysRevE.64.046212
We investigate the instabilities and bifurcations of traveling pulses in a model excitable medium; in particular we discuss three different scenarios for the loss of stability resp. the disappearance of stable pulses. In numerical simulations beyond the instabilities we observe replication of pulses (backfiring) resulting in complex periodic or spatiotemporally chaotic dynamics as well as modulated traveling pulses. We approximate the linear stability of traveling pulses through computations in a finite albeit large domain with periodic boundary conditions. The critical eigenmodes at the onset of the instabilities are related to the resulting spatiotemporal dynamics and act upon the back of the pulses. The first scenario has been analyzed earlier for high excitability resp. low excitation threshold: it involves the collision of a stable pulse branch with an unstable pulse branch in a so called T-point.
Bär Markus
Kevrekidis Ioannis G.
Krishnan J.
Or-Guil Michal
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