Abstract
Self-organized pattern formation occurs when complex spatio-temporal structures result from seemingly simple dynamical evolution processes. The formation of animal markings can be understood in this context in terms of a Turing instability. Zebra stripes, and other biological patterns, emerge in reaction-diffusion systems, which will be discussed together with the notion of self-stabilizing wavefronts, as observed for the Fisher equation.
Further prominent examples of self-organizing processes treated in this chapter involve collective decision making and swarm intelligence, as occurring in social insects and flocking birds, information offloading in terms of stigmergy, opinion dynamics and the physics of traffic flows, including the ubiquitous phenomenon of self-organized traffic congestions.
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Notes
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Recall the expression \(\mathrm {i}\hbar \frac {\partial \psi }{\partial t} = - \frac {\hbar ^2}{2m}\varDelta \psi + V \psi \) for the time-dependent one dimensional Schrödinger equation. Equation (4.23) is recovered for an exponential time dependency \(\sim \!\exp (-i\lambda t/\hbar )\) of the wavefunction \(\psi \).
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A prototypical example are the boolean networks discussed in Chap. 7.
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The classical voter model is treated in exercise (4.8).
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Gros, C. (2024). Self Organization. In: Complex and Adaptive Dynamical Systems. Springer, Cham. https://doi.org/10.1007/978-3-031-55076-8_4
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