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Robust outer synchronization between two complex networks with fractional order dynamics.

Mohammad Mostafa Asheghan¹, Joaquín Míguez, Mohammad T Hamidi-Beheshti

¹Control and Communication Networks Lab, Electrical Engineering Department, Tarbiat Modares University, Tehran, Iran. asheghan@tsc.uc3m.es

Chaos (Woodbury, N.Y.)

|October 7, 2011

Summary

This summary is machine-generated.

This study explores outer synchronization in complex networks with fractional-order dynamics. Researchers established conditions for synchronization and robust synchronization, even with parameter perturbations, using novel analytical methods.

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Area of Science:

Complex Networks
Fractional-Order Dynamics
Nonlinear Systems
Chaos Theory

Background:

Investigates synchronization phenomena in interconnected systems.
Focuses on complex networks with fractional-order differential equations governing node dynamics.
Addresses the challenge of achieving synchronization between master and response systems.

Purpose of the Study:

To analyze and establish conditions for outer synchronization in fractional-order complex networks.
To develop methods for achieving robust outer synchronization despite parameter perturbations.
To extend synchronization analysis to both fractional-order and integer-order dynamics.

Main Methods:

Analysis of synchronization error dynamics.
Application of a lemma on eigenvalues of Kronecker products.
Formulation of conditions using linear matrix inequalities (LMIs) for robust synchronization.

Main Results:

Established conditions for achieving outer synchronization in fractional-order complex networks.
Developed criteria for robust outer synchronization under bounded parameter perturbations.
Demonstrated generalized and robust outer synchronization using fractional-order Lorenz dynamics examples.

Conclusions:

The study provides a theoretical framework for outer and robust outer synchronization in fractional-order networks.
The derived conditions are applicable to a wide range of fractional-order and integer-order systems.
Numerical examples validate the effectiveness of the proposed synchronization schemes.