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Outer synchronization of coupled discrete-time networks.

Changpin Li¹, Congxiang Xu, Weigang Sun

¹Department of Mathematics, Shanghai University, Shanghai, ChinaThe School of Science, Hangzhou Dianzi University, Hangzhou, China.

Chaos (Woodbury, N.Y.)

|April 2, 2009

Summary

This study explores outer synchronization in discrete-time networks. Results show synchronization is achievable even with different network connection topologies.

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Area of Science:

Complex Networks
Systems Theory
Applied Mathematics

Background:

Synchronization phenomena are crucial in understanding coupled systems.
Discrete-time networks offer a framework for modeling various dynamic processes.
Outer synchronization is a specific type of synchronization between networks.

Purpose of the Study:

To theoretically and numerically investigate outer synchronization in discrete-time networks.
To establish criteria for achieving outer synchronization between coupled networks.
To explore synchronization capabilities when networks possess different connection topologies.

Main Methods:

Analytical derivation of a sufficient criterion for outer synchronization.
Numerical simulations to validate theoretical findings.
Exploration of synchronization in networks with non-identical connection topologies.

Main Results:

A sufficient condition for outer synchronization in networks with identical topologies was analytically derived.
Numerical examples confirmed the theoretical analysis.
Networks with different connection topologies were shown to achieve outer synchronization.

Conclusions:

Outer synchronization is achievable in discrete-time networks.
The derived criterion provides a theoretical basis for synchronization.
Network topology differences do not preclude outer synchronization.