Ikeda map

In physics and mathematics, the Ikeda map is a discrete-time dynamical system given by the complex 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 Ikeda 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 z n {displaystyle z_{n}} stands for the electric field inside the resonator at the n-th step of rotation in the resonator, and A {displaystyle A} and C {displaystyle C} are parameters which indicates laser light applied from the outside, and linear phase across the resonator, respectively. In particularthe parameter B ≤ 1 {displaystyle Bleq 1} is called dissipation parameter characterizingthe loss of resonator, and in the limit of B = 1 {displaystyle B=1} the Ikeda map becomesa conservative map.