Study on the Stability of Nonlinear Mathematical Models in Dynamic Evolution of Complex Networks

The research on the formation mechanism, geometric characteristics, evolution law and its analysis, behavior prediction and regulation of networks has gradually formed the field of complex network research, especially the research on the successive failures of complex networks has attracted extensive attention from scholars at home and abroad. In this paper, a binary nonlinear load capacity model which is closer to reality is established for the successive failures of complex power grids. The article assumes that every time there is a shortest route transmission at the same time, and each route is assumed that the load of a node exceeds the capacity of the node will be deleted. These two problems are related to communication and power grid, especially in the field of communication, power grid and so on have greater application value. By using the average field method and MATLAB software, the analytical expression of the accuracy of the method is derived, and the correctness of the two methods is proved by computer simulation. MATLAB software is used to simulate the stability of the evolution model. The results show that the new evolutionary model has strong ability to resist cascade failure. This method not only improves the robustness of the system, but also reduces the equipment investment.