''x'' span vertical slice shows attractor specific value ''r'' diagram displays period doubling ''r'' increases eventually producing chaos darker points visited frequently discrete chaotic systems logistic map exhibit strange attractors whatever dimensionality universality one dimensional maps parabolic maxima feigenbaum constants math delta math math alpha math ref name feigenbaum ref well visible map proposed toy model discrete laser dynamics math x rightarrow g x mathrm tanh x math math x math stands electric field amplitude math g math ref name okulov yu ref laser gain bifurcation parameter
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