This document summarizes a research paper that presents a framework for controlling synchronization patterns in complex networks of coupled chaotic oscillators. The framework groups network nodes into clusters and uses pinning coupling to control the large network by stabilizing unstable synchronous patterns associated with network symmetries. The approach is mathematically analyzed and demonstrated on a six-node network of coupled Lorenz oscillators, showing it can control the system's synchronous mode.

1. Controlling synchronous
patterns in complex network
Tran Quoc Hoan
@k09hthaduonght.wordpress.com/
Paper Alert 2016-04-22, Hasegawa lab., Tokyo
The University of Tokyo
PHYSICAL REVIEW E, Weijie Lin et al.,
received 9 Nov. 2015; published 18 Apr. 2016

2. Abstract
Controlling synchronous pattern 2
… a general framework and develop techniques for controlling
synchronization patterns in complex network of coupled chaotic
oscillators…control network, and use it to control the large-size
complex network by means of pinning coupling. We argue
mathematically that for any of the network symmetries, there
always exists a critical pinning strength beyond which the unstable
synchronous pattern associated to this symmetry can be
stabilized…

3. Motivation
Controlling synchronous pattern 3

4. Model
Controlling synchronous pattern 4
• Symmetric pair nodes = whose permutation does not
change the system dynamical equation
• Model coupling functiondynamic of oscillators
If connect: wij = wij else wij = 0

5. Model and Control Method
Controlling synchronous pattern 5
The network nodes are
grouped into a small
number of clusters
nl = size of Vl cluster

6. Theoretical Analysis
6Controlling synchronous pattern

7. Theoretical Analysis
7

8. Theoretical Analysis
8
without
control
without
control
| s
2| < min | s
2| > min
transverse mode
controlling model
the synchronous model

9. Six-node network of coupled chaotic Lorenz oscillators
9

10. Theoretical Analysis
10

11. Reference links
11
• …
Controlling synchronous pattern