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Formation and propagation of localized states in extended systems

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.