Network modeling characterizes the underlying principles of structural
properties and is of vital significance for simulating dynamical processes in
real world. However, bridging structure and dynamics is always challenging due
to the multiple complexities in real systems. Here, through introducing the
individual's activity rate and the possibility of group interaction, we propose
a probabilistic activity driven (PAD) model that could generate temporal
higher-order networks with both power-law and high-clustering characteristics,
which successfully links the two most critical structural features and a basic
dynamical pattern in extensive complex systems. Surprisingly, the power-law
exponents and the clustering coefficients of the aggregated PAD network could
be tuned in a wide range by altering a set of model parameters. We further
provide an approximation algorithm to select the proper parameters that can
generate networks with given structural properties, the effectiveness of which
is verified by fitting various real-world networks. Lastly, we explore the
co-evolution of PAD model and higher-order contagion dynamics, and analytically
derive the critical conditions for phase transition and bistable phenomenon.
Our model provides a basic tool to reproduce complex structural properties and
to study the widespread higher-order dynamics, which has great potential for
applications across fields