Delay coupling enhances synchronization in complex networks

¹ Institute for Physics, Humboldt University - 12489 Berlin, Germany, EU
² Potsdam Institute for Climate Impact Research - 14473 Potsdam, Germany, EU
³ Institute for Complex Systems and Mathematical Biology, University of Aberdeen - Aberdeen, UK, EU

^a skumarusnld@gmail.com

Received: 22 November 2011
Accepted: 29 February 2012

Abstract

The phenomenon of enhancement of synchronization due to time delay is investigated in an arbitrary delay coupled network with chaotic units. Using the master stability formalism for a delay coupled network, we elaborate that there always exists an extended regime of stable synchronous solutions of the network for appropriate coupling delays. Further, the stable synchronous state is achieved even at smaller values of coupling strength with delay, which can be only attained at much larger coupling strength without delay. This also facilitates the increase in the number of synchronized nodes in the delay coupled network beyond size instability of the same network without delay. Further, the largest transverse Lyapunov exponents in the master stability surface of the network clearly demarcates the stable synchronous solutions from the unstable ones. The generic nature of our results is also corroborated using three paradigmatic models, namely, Rössler and Lorenz systems as well as Hindmarsh-Rose neurons as nodes in the delay coupled network.