page_title: Ikeda map
section_title: Point trajectories
hierarchical_section_title: Ikeda map / Point trajectories
caption_attribution_description: English: Ikeda trajectory plot made using MATLAB
context_page_description: In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex map
  The original map was proposed first by Kensuke Ikeda as a model of light going around
  across a nonlinear optical resonator in a more general form. It is reduced to the above simplified "normal" form by Ikeda, Daido and Akimoto stands for the electric field inside the resonator at the n-th step of rotation in the resonator, and and are parameters which indicate laser light applied from the outside, and linear phase across the resonator, respectively. In particular
  the parameter is called dissipation parameter characterizing
  the loss of resonator, and in the limit of the Ikeda map becomes
  a conservative map.
  The original Ikeda map is often used in another modified form in order
  to take the saturation effect of nonlinear dielectric medium into account:
  A 2D real example of the above form is:
  where u is a parameter and
  For, this system has a chaotic attractor.
context_section_description: The plots below show trajectories of 200 random points for various values of . The inset plot on the left shows an estimate of the attractor while the inset on the right shows a zoomed in view of the main trajectory plot.
caption: u = 0.65
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