Cluster synchronization of fractional-order two-layer networks and application in image encryption/decryption

Area of Science:

• Complex Networks
• Chaos Theory
• Fractional Calculus

Background:

• Investigating synchronization in complex networks is crucial for understanding emergent behaviors.
• Fractional-order systems offer richer dynamics compared to their integer-order counterparts.
• Layered network structures present unique challenges for synchronization analysis.

Purpose of the Study:

• To develop and analyze a fractional-order two-layer network model.
• To achieve finite-time cluster synchronization in distinct network layers.
• To propose a secure encryption/decryption scheme based on network synchronization.

Main Methods:

• Construction of a fractional-order two-layer network with distinct topologies.
• Application of a fractional-order finite-time convergence lemma for synchronization.
• A novel collective node treatment strategy for analyzing cluster synchronization.

Main Results:

• Successful implementation of finite-time cluster synchronization in the first layer.
• Demonstration of a new analytical insight into fractional-order two-layer network synchronization.
• Validation of theoretical findings through three illustrative examples.

Conclusions:

• The proposed fractional-order two-layer network model enables effective finite-time cluster synchronization.
• The novel analytical approach provides significant insights into complex network dynamics.
• The developed encryption/decryption scheme offers enhanced security leveraging chaotic sequences.