Design of coupling for synchronization in time-delayed systems

Abstract

We report a design of delay coupling for targeting desired synchronization in delay dynamical systems. We target synchronization, antisynchronization, lag-, antilag- synchronization, amplitude death (or oscillation death) and generalized synchronization in mismatched oscillators. A scaling of the size of an attractor is made possible in different synchronization regimes. We realize a type of mixed synchronization where synchronization, antisynchronization coexist in different pairs of state variables of the coupled system. We establish the stability condition of synchronization using the Krasovskii-Lyapunov function theory and the Hurwitz matrix criterion. We present numerical examples using the Mackey-Glass system and a delay Rössler system.

8 pages, 6 figures; Chaos 22 (2012)

References in corpus (8)

• Zero-lag long-range synchronization via dynamical relaying
• Crowd synchrony and quorum sensing in delay-coupled lasers
• Adaptive synchronization of coupled chaotic oscillators
• Using synchronization of chaos to identify the dynamics of unknown systems
• Stability of synchronization in coupled time-delay systems using Krasovskii-Lyapunov theory
• Constructing Generalized Synchronization Manifolds by Manifold Equation
• Lag synchronization and scaling of chaotic attractor in coupled system
• Intermittency transition to generalized synchronization in coupled time-delay systems

Cited by in corpus (6)

• Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion
• Synchronization of two coupled multimode oscillators with time-delayed feedback
• Generalized counter-rotating oscillators: Mixed synchronization
• Mixed mode oscillation suppression states in coupled oscillators
• How to induce multiple delays in coupled chaotic oscillators?
• The role of intermediaries in the synchronization of pulse-coupled oscillators