Probabilistic activity driven model of temporal simplicial networks and its application on higher-order dynamics

Area of Science:

• Complex Systems Science
• Network Science
• Statistical Physics

Background:

• Network modeling is crucial for simulating dynamical processes but bridging structure and dynamics remains challenging.
• Real-world systems exhibit complex structural properties like power-law distributions and high clustering.
• Understanding these properties is vital for accurate modeling of system behavior.

Purpose of the Study:

• To propose a probabilistic activity-driven (PAD) model that integrates individual activity and group interactions.
• To generate temporal higher-order networks exhibiting both power-law and high-clustering characteristics.
• To investigate the co-evolution of network structure and higher-order contagion dynamics.

Main Methods:

• Development of the probabilistic activity-driven (PAD) model incorporating individual activity rates and group interactions.
• Parameter tuning to control power-law exponents and clustering coefficients in generated networks.
• Construction of a co-evolution framework with higher-order contagion dynamics, analyzed using theoretical and numerical methods.

Main Results:

• The PAD model successfully generates temporal higher-order networks with tunable power-law and high-clustering properties.
• An approximation algorithm was developed and validated for generating networks with specific structural characteristics.
• Analysis of contagion dynamics revealed that higher-order interactions can promote bistability but delay outbreaks under heterogeneous activity rates.

Conclusions:

• The PAD model provides a versatile tool for reproducing complex network structures and studying higher-order dynamics.
• The findings offer insights into the interplay between network topology, individual behavior, and emergent dynamics.
• The model has significant potential for applications in diverse fields requiring the analysis of complex systems.