title: Exact synchronization bound for coupled time-delay systems.
abstract: We obtain an exact bound for synchronization in coupled time-delay systems using the generalized Halanay inequality for the general case of time-dependent delay, coupling, and coefficients. Furthermore, we show that the same analysis is applicable to both uni- and bidirectionally coupled time-delay systems with an appropriate evolution equation for their synchronization manifold, which can also be defined for different types of synchronization. The exact synchronization bound assures an exponential stabilization of the synchronization manifold which is crucial for applications. The analytical synchronization bound is independent of the nature of the modulation and can be applied to any time-delay system satisfying a Lipschitz condition. The analytical results are corroborated numerically using the Ikeda system.
authors.affiliation: Potsdam Institute for Climate Impact Research, 14473 Potsdam, Germany.
authors.forename: D V
authors.initials: DV
authors.lastname: Senthilkumar
authors.forename: Luis
authors.initials: L
authors.lastname: Pesquera
authors.forename: Santo
authors.initials: S
authors.lastname: Banerjee
authors.forename: Silvia
authors.initials: S
authors.lastname: Ortín
authors.forename: J
authors.initials: J
authors.lastname: Kurths
mesh_terms: D017711:Nonlinear Dynamics; D013997:Time Factors