Synchronization transitions in adaptive simplicial complexes with cooperative and competitive dynamics

Area of Science:

• Complex systems
• Network science
• Statistical physics

Background:

• Current adaptive network models often overlook higher-order interactions and varied adaptation types (cooperative/competitive).
• These neglected factors are crucial in real-world systems like the human brain and social networks.
• Understanding these dynamics is key to explaining collective behaviors such as synchronization.

Purpose of the Study:

• To develop an adaptive network model incorporating higher-order interactions and both cooperative and competitive adaptations.
• To investigate the impact of these combined factors on collective properties, particularly synchronization phase transitions.
• To explore how network structure and adaptation types dictate the manner and timing of synchronization.

Main Methods:

• Development of a simplified adaptive network model.
• Analysis of phase transitions, focusing on synchronization phenomena.
• Investigation of the influence of higher-order interactions and coupling strengths on system dynamics.
• Examination of systems with only competitive adaptations versus those with combined cooperative and competitive adaptations.

Main Results:

• Higher-order interactions can shift synchronization from first-order to second-order under competitive adaptation.
• Synchronization is possible even without pairwise interactions if higher-order coupling is sufficiently strong.
• Competitive adaptations lead to second-order-like phase transitions and clustering.
• Combined cooperative and competitive adaptations result in a first-order-like phase transition with hysteresis.

Conclusions:

• The model successfully captures complex synchronization dynamics influenced by higher-order interactions and diverse adaptation types.
• The findings demonstrate that network structure and adaptation mechanisms can be tuned to control synchronization onset and behavior.
• This work provides a more comprehensive framework for understanding collective phenomena in adaptive systems.