Ikeda map
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 as a model of light going around across a nonlinear optical resonator (ring cavity containing a nonlinear dielectric medium) 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 particularthe parameter is called dissipation parameter characterizingthe loss of resonator, and in the limit of the Ikeda map becomesa conservative map. The original Ikeda map is often used in another modified form in orderto 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. (Wikipedia).
