.. _sphx_glr_api_gallery_fractals_chaos_lyapunov:

Lyapunov exponents
-------------------

Estimating the Lyapunov exponent of 1D maps and simple flows.


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    <div class="sphx-glr-thumbcontainer" tooltip="Sweeps the logistic map&#x27;s growth-rate parameter r and estimates the Lyapunov exponent at each value: negative in the periodic windows, crossing zero exactly at each bifurcation, and mostly positive beyond the onset of chaos at r ~ 3.56995.">

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  :doc:`/api/gallery/fractals_chaos/lyapunov/plot_01_logistic_map_route_to_chaos`

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      <div class="sphx-glr-thumbnail-title">Lyapunov exponent across the logistic map's route to chaos</div>
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   /api/gallery/fractals_chaos/lyapunov/plot_01_logistic_map_route_to_chaos