Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
40/2007

Adaptive dynamical networks via neighborhood information: synchronization and pinning control

Wenlian Lu

Abstract

In this paper, we introduce a model of adaptive dynamical network by integrating the complex network model and adaptive technique. This model is characterized by that the adaptive updating laws for each vertex in the network depend only on the state information of its neighborhood besides itself and external controllers. This suggests that adaptive technique be added to a complex network without breaking its intrinsic existing network topology. The core of adaptive dynamical networks is to design suitable adaptive updating laws to attain certain aims. Here, we propose two series of adaptive laws to synchronize and pin a complex network respectively. Based on the Lyapunov function method, we can prove that under several mild conditions, with the adaptive technique, a connected network topology is sufficient to synchronize or stabilize any chaotic dynamics of the uncoupled system. This implies that these adaptive updating laws actually enhance synchronizability and stabilizability respectively. We find out that even though these adaptive methods can success for all networks with connectivity, the underlying network topology can affect the convergent rate and the terminal average coupling and pinning strength. And, this influence can be measured by the smallest nonzero eigenvalue of the corresponding Laplacian. Moreover, we detailed study the influence of the prior parameters in this adaptive laws and present several numerical examples to verify our theoretical results and further discussions.

Received:
Apr 17, 2007
Published:
Apr 17, 2007
PACS:
05.45.Gg, 05.45.Xt, 02.30.Hq
Keywords:
adaptive complex networks, synchronization, pinning control

Related publications

inJournal
2007 Repository Open Access
Wenlian Lu

Adaptive dynamical networks via neighborhood information: synchronization and pinning control

In: Chaos, 17 (2007) 2, p. 023122