The Ikeda differential equation is a scalar delay differential equation with sinusoidal delayed feedback. A form used to model an optical resonator is
![x^'(t)=-gammax(t)+musin[x(t-tau)-c],](/images/equations/IkedaDifferentialEquation/NumberedEquation1.svg) |
where 
is the derivative with respect to time 
, 
is the relaxation rate, 
is the delay, 
is the feedback strength, and 
is a phase offset (Ikeda and Matsumoto
1987, Kubyshkin and Moriakova 2018). For a constant solution 
, the equation reduces to 
. With 
, the linearization about 
is 
.
An exponential perturbation 
therefore gives the characteristic
equation
 |
For appropriate parameter values, the nonlinear equation can exhibit multiple stable periodic orbits and chaos (Ikeda and Matsumoto 1987).
