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Formation and propagation of localized states in extended systems. (English) Zbl 1108.35386
Summary: We study a one-species-diffusion equation supplemented by a nonlinear saturation term. If this term includes temporal delay, a rich spatio-temporal behavior already at the critical point where the steady homogeneous solution gets unstable is expected. Normal form transformation into a complex Ginzburg-Landau equation shows that the condition for phase turbulence is always fulfilled. As a secondary instability of these chaotic states well ordered spiral waves and targets are found numerically. Here the system shows features well-known from excitable media. Finally we propose the construction of logical circuits by means of a network built up by one-dimensional excitable media.
35Q80Appl. of PDE in areas other than physics (MSC2000)
92C15Developmental biology, pattern formation