title: Finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems.
abstract: We introduce a method for the calculation of finite-time Lyapunov exponents in time-delayed nonlinear dynamical systems. We apply the method to the Mackey-Glass model with time-delayed feedback. We investigate the standard deviation of the probability distribution of the finite-time Lyapunov exponents when the finite time or the delay time is changed. It is found that the standard deviation decreases in a power-law scaling with the exponent ∼0.5 as the finite time or the delay time is increased. Similar results are obtained for the finite-time Lyapunov spectrum.
authors.affiliation: Department of Information and Computer Sciences, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama City, Saitama, 338-8570, Japan.
authors.forename: Kazutaka
authors.initials: K
authors.lastname: Kanno
authors.affiliation: Department of Information and Computer Sciences, Saitama University, 255 Shimo-okubo, Sakura-ku, Saitama City, Saitama, 338-8570, Japan.
authors.forename: Atsushi
authors.initials: A
authors.lastname: Uchida