Aperiodically intermittent event-triggered pinning control on cluster synchronization of directed complex networks

Area of Science:

• Complex networks
• Nonlinear systems
• Control theory

Background:

• Complex networks exhibit emergent behaviors like cluster synchronization.
• Non-identical nodes and asymmetrical coupling pose challenges to synchronization.
• Existing control methods may not be efficient for dynamic network topologies.

Purpose of the Study:

• To investigate exponential cluster synchronization in nonlinearly coupled complex networks with non-identical nodes.
• To develop a novel aperiodically intermittent pinning control (APIPC) protocol tailored for cluster-tree topologies.
• To integrate an event-triggered mechanism (ETM) for optimized control instants.

Main Methods:

• Aperiodically intermittent pinning control (APIPC) targeting specific nodes in directional links between clusters.
• Event-triggered mechanism (ETM) to determine control application based on system states.
• Minimal control ratio and segmentation analysis for deriving synchronization conditions.
• Rigorous analysis to exclude Zeno behavior in the ETM.

Main Results:

• Sufficient conditions for achieving exponential cluster synchronization are derived.
• The proposed APIPC protocol effectively synchronizes non-identical nodes in complex networks.
• The ETM successfully optimizes control application without Zeno behavior.
• Numerical simulations validate the effectiveness of the control strategy.

Conclusions:

• The developed APIPC with ETM is an effective strategy for exponential cluster synchronization in complex networks.
• The method offers advantages in terms of control efficiency and applicability to dynamic network structures.
• The findings contribute to the understanding and control of synchronization phenomena in networked systems.