Emergence of Turing patterns in complex networks: A partial link activation approach.

Area of Science:

• Complex Systems
• Network Science
• Mathematical Biology

Background:

• Turing patterns are a key example of self-organization in nature.
• Existing models for pattern formation in reaction-diffusion networks typically assume uniform diffusion coefficients across all links.
• The role of partial link activation in pattern formation remains underexplored.

Purpose of the Study:

• To investigate the emergence of Turing patterns in reaction-diffusion networks using a partial link activation approach.
• To compare the effectiveness of random versus targeted activation schemes for inducing pattern formation.
• To explore the conditions for pattern formation when only a subset of network links is activated.

Main Methods:

• Utilized mean-field theory to derive conditions for pattern formation under random link activation.
• Employed numerical simulations to compare random and targeted activation strategies.
• Investigated pattern formation in network-organized reaction-diffusion systems.

Main Results:

• Partial link activation can successfully generate Turing patterns.
• Targeted activation schemes demonstrate superior performance in promoting pattern formation compared to random activation.
• Demonstrated that local regulation can influence global network dynamics.

Conclusions:

• Pattern formation is achievable through partial activation of network links, offering a more efficient mechanism.
• Targeted activation provides a more effective strategy for inducing Turing patterns than random activation.
• This research offers novel insights into how local regulatory mechanisms impact large-scale network behaviors.