Abstract
we consider a lattice system of identical oscillators that are all coupled to one another with a diffusive coupling that has a time lag. We use the natural splitting of the system into synchronized manifold and transversal manifold to estimate the value of the time lag for which the stability of the system follows from that without a time lag. Each oscillator has a unique periodic solution that is attracting.
Highlights
In the past few years, there have been many papers concerned with the synchronization and stability of systems with diffusive coupling
Let us suppose that we have n subsystems z j ∈ Rd, j = 1, 2,..., n, with the dynamics of each z j given by the solutions of the system of d first order equations
In order to prove the theorem on the stability of a synchronization manifold with a small delay, we need to state a lemma that will be useful in the estimate of the delay r for which stability synchronized manifold can be
Summary
In the past few years, there have been many papers concerned with the synchronization and stability of systems with diffusive coupling (see for instance Afraimovich et al, 1983, 1986, Chow and Liu 1977, Hale 1977, Wasike 2003, 2007, and references therein). Let us suppose that we have n subsystems z j ∈ Rd , j = 1, 2,..., n, with the dynamics of each z j given by the solutions of the system of d first order equations Let A ∞ be the global attractor for the equation z (t ) = f ( z (t ))
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Sultan Qaboos University Journal for Science [SQUJS]
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
