Ikeda Map

The Ikeda map is a discrete time dynamical system on the complex plane, or equivalently on a two dimensional real plane, in which each point is transformed into a new point by a formula combining rotation by an amount that depends on the point's distance from the origin with a fixed complex offset. It was introduced in 1979 by the Japanese physicist Kensuke Ikeda as a model of the behavior of light circulating inside a nonlinear optical ring cavity, a physical system in which the phase of light shifts in a way that depends on its own intensity. For a suitable range of its parameters the map produces a strange attractor, a bounded region of the plane that orbits approach and then wander across chaotically without ever repeating exactly, and the distinctive swirled, spiral shaped attractor the map generates made it, alongside the Lorenz and Henon systems, one of the standard illustrative examples used to introduce deterministic chaos and strange attractors.