Bifurcations in a system described by a nonlinear differential equation with delay

Computer simulations of a nonlinear differential equation with time delay have been carried out to determine the possible steady states over a wide range of parameter values. A variety of nonlinear phenomena, including chaotic attractors and multiple coexisting attractors, are observed. Precision of the solutions is verified by means of evaluating the computational error at each time step. A number of bifurcations are observed, and the involvement of unstable periodic orbits is confirmed. The phase space of the system is infinite dimensional, but nonetheless all the bifurcation phenomena observed, including the blue sky disappearance (boundary crisis) of a chaotic attractor, show geometric structures which are consistent with familiar low-dimensional center-manifold descriptions.