Output Synchronization of Complex Dynamical Networks With Multiple Output or Output Derivative Couplings

Area of Science:

• Control Theory
• Network Science
• Dynamical Systems

Background:

• Complex dynamical networks (CDNs) are crucial in various fields, but achieving synchronized behavior, especially output synchronization, remains challenging.
• Existing methods often struggle with networks featuring multiple output or output derivative couplings.

Purpose of the Study:

• To develop a criterion for output synchronization in CDNs with multiple output couplings (CDNMOCs).
• To design an adaptive control scheme to guarantee output synchronization in CDNMOCs.
• To extend the adaptive output synchronization approach to CDNs with multiple output derivative couplings.

Main Methods:

• Lyapunov functional and inequality techniques are employed to establish the output synchronization criterion.
• An adaptive control scheme is designed based on the derived criterion.
• Numerical simulations are used to validate the effectiveness of the proposed control strategy.

Main Results:

• An output synchronization criterion for CDNMOCs is successfully derived.
• An effective adaptive control scheme is proposed for CDNMOCs.
• The approach is demonstrated to be effective for CDNs with multiple output derivative couplings.

Conclusions:

• The proposed Lyapunov-based methods and adaptive control schemes effectively achieve output synchronization in complex dynamical networks.
• The findings provide a robust framework for controlling synchronization in networked systems with intricate coupling structures.