Emergent order in adaptively rewired networks.

Area of Science:

• Complex Systems
• Network Science
• Chaos Theory

Background:

• Complex networks often exhibit intricate dynamical states.
• Controlling these states, particularly chaos, is crucial for system stability and function.
• Adaptive mechanisms are needed to navigate vast configuration spaces for desired network behavior.

Purpose of the Study:

• To propose and evaluate adaptive link change strategies for achieving ordered dynamical states in complex networks.
• To investigate feedback mechanisms based on global synchronization error for network adaptation.
• To demonstrate the effectiveness of these strategies in suppressing chaos within coupled chaotic map systems.

Main Methods:

• Two adaptive strategies were proposed: threshold-based and error-proportional link changes.
• Global synchronization error was used as feedback to guide network connectivity adjustments.
• The strategies were tested on two prototypical systems of coupled chaotic maps.

Main Results:

• Both adaptive strategies successfully guided networks to chaos suppression within a defined tolerance.
• A sharply defined transition to low mean synchronization error was observed after a critical coupling strength.
• The time and fraction of link adaptation decreased significantly, indicating convergence to stable, ordered configurations.

Conclusions:

• Adaptive link change strategies are effective for efficient search and discovery of network configurations yielding targeted dynamics.
• These methods offer potential for controlling extended interactive systems and understanding natural regularization mechanisms in complex networks.
• The findings highlight the role of feedback-based adaptation in achieving desired network states and suppressing undesirable dynamics like chaos.