Abstract

A method is proposed to describe bifurcations in high-dimensional problems. The saturable ring cavity driven by a retarded feedback is studied as an example of retarded differential difference device. The main stage of the treatment is the calculation of the Lyapunov separation vectors as an orthogonal basis for the system. These vectors span the unstable and stable directions of the linearized equations. They are generated by the Gram–Schmidt procedure¹ which provides Lyapunov exponents arranged in decreasing order. This fortunate property allows the reduction of problems posed in infinite dimensional spaces to low dimensional ones defined by the set of Lyapunov vectors which carry the relevant information about the bifurcation.

© 1988 Optical Society of America