Abstract

Ring-cavity delay-differential equations, first derived by Ikeda,¹ are studied without any approximation. We focus on the instabilities in the limit where the delay time τ_R is much larger than the decay time T₁. We compare the complex field amplitude solution E(t) of the infinite dimensional dynamical system with the solution E[(n + 1 )τ_R] = f[E(nτ_R)] of the 2-D mapping resulting from the adiabatic following approximation.² Chaos of the infinite-dimensional system does not arise from a period-doubling sequence, in disagreement with the 2-D mapping scenario.³ The chaotic attractor [lmE(t_i) vs ReE(t_i) for many t_i, in each τ_R and for many τ_R] for the 2-D mapping is a spiral. The chaotic attractors of the infinite-dimensional system are much more complex. They can be described crudely as fuzzed-out spirals which do not appear to change for τ_R /T₁ > 5, suggesting that the Lyapunov dimension of the attractors saturates. If so, this behavior differs markedly from the linear dependence on τ_R /T₁ found for the Mackey-Glass delay-differential equation,⁴ removing hope of finding a simple variation law vs τ_R, whatever the nonlinear flux may be.

© 1985 Optical Society of America