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Overcoming network resilience to synchronization through non-fast stochastic broadcasting.

Russell Jeter¹, Maurizio Porfiri², Igor Belykh¹

¹Department of Mathematics and Statistics, Georgia State University, P.O. Box 4110, Atlanta, Georgia 30302-4110, USA.

Chaos (Woodbury, N.Y.)

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Summary

Stochastic broadcasting can synchronize networks, but timing is key. Researchers found specific switching periods, influenced by network structure, create "windows of opportunity" for synchronization.

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Area of Science:

Network Science
Chaos Theory
Control Theory

Background:

Stochastic broadcasting is an understudied method for network control.
Internal network connections enhance resilience to external synchronization attempts.

Purpose of the Study:

To investigate the feasibility of on-off stochastic broadcasting for inducing network synchronization.
To analyze the interplay between network topology and broadcasting switching periods.

Main Methods:

Mathematical analysis of a target network with a single reference node.
Derivation of a synchronization criterion based on network properties and broadcasting parameters.
Utilizing coupled chaotic tent maps as a test-bed.

Main Results:

A complex relationship exists between network topology and broadcasting switching periods affecting synchronization.
Synchronization depends explicitly on the network's Laplacian spectrum and broadcasting parameters.
"Windows of opportunity" for synchronization emerge, favoring non-fast switching periods.

Conclusions:

The Laplacian spectrum and broadcasting switching period critically influence synchronization.
Specific switching periods must be manipulated to achieve synchronization, with zero and largest eigenvalues being key for tent maps.