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Age-dependent Dynamics of Locomotion in Caenorhabditis elegans: A Lyapunov Exponent Analysis

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Synchronization and local convergence analysis of networks with dynamic diffusive coupling.

Daniel Alberto Burbano Lombana¹, Mario di Bernardo¹

¹Department of Electrical Engineering and Information Technology, University of Naples Federico II, Naples 8125, Italy.

Chaos (Woodbury, N.Y.)

|December 3, 2016

Summary

This study introduces novel dynamic coupling strategies, proportional-integral (PI) and proportional-derivative (PD) laws, to enhance synchronization in nonlinear networks. These methods improve network performance, especially with nonidentical node dynamics.

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Area of Science:

Complex Systems
Network Science
Nonlinear Dynamics

Background:

Achieving synchronization in networks of nonlinear units is a significant challenge.
Traditional diffusive coupling methods may not be sufficient for complex or nonidentical systems.
Dynamic coupling terms offer potential for improved network synchronization.

Purpose of the Study:

To develop and analyze novel dynamic diffusive coupling strategies for network synchronization.
To investigate the effectiveness of proportional-integral (PI) and proportional-derivative (PD) coupling laws.
To extend the Master Stability Function approach for analyzing networks with dynamic links.

Main Methods:

Introduction of two dynamic coupling terms: integral or derivative of state mismatches.
Formulation of distributed PI and PD control laws for network coupling.
Extension of the Master Stability Function (MSF) for stability analysis of dynamic networks.

Main Results:

The proposed PI and PD dynamic coupling strategies effectively improve network synchronization.
These methods demonstrate robustness, particularly for networks with nonidentical node dynamics.
Stability analysis using the extended MSF confirms the effectiveness of the dynamic coupling.

Conclusions:

Dynamic diffusive coupling, specifically PI and PD laws, offers a powerful approach to enhance synchronization in nonlinear networks.
The extended Master Stability Function provides a reliable tool for analyzing the stability of such dynamic networks.
The validated methods show promise for applications involving complex systems like chaotic Lorenz systems and nonlinear mechanical systems.