Feedback Pinning Control of Successive Lag Synchronization on a Dynamical Network

Area of Science:

• Complex Systems
• Control Theory
• Dynamical Networks

Background:

• Successive lag synchronization (SLS) is a critical phenomenon in natural and social systems.
• Existing control theory for SLS is underdeveloped compared to other synchronization patterns.

Purpose of the Study:

• To develop effective control strategies for achieving SLS in complex dynamical networks.
• To address the lack of control theory for SLS and enhance synchronization capabilities.

Main Methods:

• Introduction of a complex dynamical network model with distributed delayed couplings.
• Design of linear feedback pinning control and adaptive feedback pinning control.
• Extension of control strategies to accommodate time-varying delays.

Main Results:

• Sufficient conditions for achieving globally stable SLS to a desired trajectory were derived.
• A control flow for SLS was established, guiding the selection of pinned nodes and feedback gains.
• Proposed pinning control schemes demonstrated feasibility with time-varying delays upon adjustment.

Conclusions:

• The study successfully advances the control theory of SLS in complex dynamical networks.
• The developed methods offer practical approaches for achieving and maintaining stable SLS.
• The findings are validated through simulations on neural networks and coupled Chua's circuits.