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Robust global synchronization of two complex dynamical networks.

Mohammad Mostafa Asheghan¹, Joaquín Míguez

¹Department of Signal Theory and Communications, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain. asheghan@tsc.uc3m.es

Chaos (Woodbury, N.Y.)

|July 5, 2013

Summary

This summary is machine-generated.

We introduce outer synchronization for coupled complex dynamical networks using matrix eigendecomposition and Lyapunov functions. This method guarantees global synchronization, independent of initial conditions, and offers robustness to model errors.

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Area of Science:

Complex dynamical networks
Network synchronization
Chaos theory

Background:

Investigating synchronization in coupled complex dynamical networks is crucial for understanding emergent behaviors.
Outer synchronization is a specific type of synchronization relevant to coupled systems.

Purpose of the Study:

To develop a theoretical framework for achieving outer synchronization in coupled complex dynamical networks.
To establish a sufficient condition for global outer synchronization, independent of initial network states.

Main Methods:

Utilizing a lemma on eigendecomposition of matrices derived from Kronecker products.
Employing a Lyapunov function tailored to the synchronization error dynamics.
Formulating the synchronization condition as a linear matrix inequality.

Main Results:

A theorem proving sufficient conditions for outer synchronization is established.
The derived condition guarantees global synchronization regardless of initial network states.
The synchronizer gain matrix is designed to be independent of network size, simplifying practical implementation.

Conclusions:

The proposed method provides a robust approach to outer synchronization for complex dynamical networks.
The framework allows for simplified synchronizer design and is resilient to model parameter errors.
Numerical simulations with Lorenz networks demonstrate the effectiveness of the outer synchronization strategy.