Nonlinear dynamic evolution and control in a new scale-free networks modeling

The nonlinear evolving and controlling in complex networks are an important way to understand the dynamic mechanism for real networks. In order to explore universality of scale-free systems, we propose an extended network model based on Barabási–Albert model by developing and decaying networks. The novel network evolves by growing and optimizing processes, such as the addition of new nodes and edges, or deletion of edges at every time step. Meanwhile, in order to describe more realistic phenomena of reality, we introduce the fitness to reflect the competition and local event of inner anti-preferential mechanism to delete the edges. We calculate analytically the degree distribution and find that the Barabási–Albert model is only one of its special cases and the model self-organizes into scale-free networks, moreover, the numerical simulations are in good agreement with the analytical conclusions. The results imply that this extended model has more comprehensive and universal simulation and reflection in complex network topology characters and evolution with practices and applications.