Evaluation of the largest Lyapunov exponent in dynamical systems with time delay

The method of estimation of the largest Lyapunov exponents for dynamical systems with time delay has been developed. This method can be applied both for flows and discrete maps. Our approach is based on the phenomenon of synchronization of identical systems coupled by linear negative feedback mechanism (flows) and exponential perturbation (maps). The existence of linear dependence of the largest Lyapunov exponent on the coupled parameter allows the precise estimation of this exponent.