Topological control of synchronous patterns in systems of networked chaotic oscillators

Abstract

Recent studies of network science have revealed the sensitive dependence of the network collective behaviors on structures, here we employ this feature of topological sensitivity for the purpose of pattern control. By simple models of networked chaotic oscillators, we are able to argue and demonstrate that, by manipulating just a single link in the network, the synchronous patterns of the system can be effectively adjusted or controlled. In particular, by changing the weight or the connection of a shortcut link in the network, we find that not only various stable synchronous patterns can be generated from the system, but also the synchronous patterns can be successfully switched among different forms. The stability of the synchronous patterns is analyzed by the method of eigenvalue analysis, and the feasibility of the control is verified by numerical simulations. Our study provides a step forward to the control of sophisticated collective behaviors in more complex networks, as well as giving insights to the evolution and function of some realistic complex systems.

Cluster synchronization and isolated desynchronization in complex networks with symmetries

“…If it is also stable, this is the case of ID. This argument is easily generalized to the case when H k permutes nodes of several clusters as this will just add other similar sums to equation (6). The latter case explains the intertwined desynchronization in the experiment and is a more general form of ID.…”

“…Equally important, and perhaps more ordinary, is partial or cluster synchronization (CS), in which patterns or sets of synchronized elements emerge 3 . Recent work on CS has been restricted to networks where the synchronization pattern is induced either by tailoring the network geometry or by the intentional introduction of heterogeneity in the time delays or node dynamics [4][5][6][7][8][9][10][11] . These anecdotal studies illustrate the interesting types of CS that can occur, and suggest a broader relationship between the network structure and synchronization patterns.…”

“…The non-trivial clusters are the nodes [1,8], [2,3,7,9], [4,6], [5,10] (the numbering of nodes matches the row and column numbers of A). The transformation matrix is …”

Synchronization of chaotic systems

“…Many versions of CS have been displayed. [48][49][50][51][52][53][54][55][56] These involve many different scenarios (unidirectional coupling, time delays, special network structures, etc. ), many of which are engineered to yield certain cluster synchronization patterns.…”

Cluster synchronization in complex network of coupled chaotic circuits: An experimental study

“…Yet recent studies give the accumulating evidences which show that cluster synchronization is also observable in complex networks [17,18,[35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. The first batch of evidences come from the synchronization of small-size complex network possessing reflection symmetries [14,17,19,40,42], where it is found, in spite of the presence of random shortcut links, the oscillators can be synchronized in pairs according to the network reflection symmetries. Additional evidences from large-size complex network possessing permutation symmetries have been also provided [43][44][45][46][47][48].…”