In the present study, some perturbation methods are applied to Duffing equations having a displacement time-delayed variable to study the stability of such systems. Two approaches are considered to analyze Duffing oscillator having a strong delayed variable. The homotopy perturbation method is applied through the frequency analysis and nonlinear frequency is formulated as a function of all the ...

Time-delay is ubiquitous in many dynamical systems. The role of single and multiple time-delay on vibrational resonance in a single Duffing oscillator and in a system of n Duffing oscillators coupled unidirectionally and driven by both a lowand a high-frequency periodic force is presented. The investigation is performed through both theoretical approach and numerical simulation. Theoretically d...

Synchronization in a bidirectionally coupled system with a finite time-delay in coupling is studied using Josephson junction as a model system. Using the LyapunovKrasovskii method a sufficient condition for the stability of synchronization is obtained and it is found to be independent of the time-delay. The sum of the Lyapunov exponents transverse to the synchronization manifold is evaluated. N...

We propose a necessary condition for the successful stabilization of a periodic orbit, using the extended version of time-delayed feedback control. This condition depends on the number of real Floquetmultipliers larger than unity and is therefore related to the wellknown odd-number limitation in non-autonomous systems. We show that the period of the orbit that is induced by mismatching the dela...

This paper is concerned with the problem of synchronization for complex dynamic networks with state and coupling time-delays. Therefore, larger class and more complicated complex dynamic networks can be considered for the synchronization problem. Based on the Lyapunov-Krasovskii functional, a delay-independent criterion is obtained and formulated in the form of linear matrix inequalities (LMIs)...

We discuss experimental demonstrations of chaotic communication in several optical systems. In each, an erbium-doped fiber ring laser (EDFRL) produces chaotic fluctuations of light intensity onto which is modulated a message consisting of a sequence of pseudorandom digital bits. This combination of chaos and message propagates at a wavelength of ∼ 1.5 microns through standard single-mode optica...

1Department of Civil Engineering; Aerospace and Mechanical Engineering; Mathematics; and Information and Operations Management; University of Southern California; Los Angeles; CA 90089-1453; U.S.A. 2Department of Aerospace and Mechanical Engineering; University of Southern California; Los Angeles; CA 90089-1453; U.S.A. 3Structural Analysis and Research Corporation; 5000 McKnight Road; Pittsburg...

This work provides one of the first attempts to derive computationally tractable criteria for analyzing the stability of Linear Parameter Varying (LPV) time-delayed systems. We present both delay-independent and delay-dependent stability conditions, which are derived using appropriately selected Lyapunov-Krasovskii functionals. According to the system parameter dependence, these functionals can...