The Structure and Evolution of Incomplete Competitive System Based on a Random Choice Mechanism

Under the presupposition of competition level keeping unchangeable, we construct a random evolution model of Incomplete Competitive System to explore its structure, nature and evolution behavior based on the random choice mechanism to competitors by mathematical analysis and numerical simulation. In this model, the death probability of node keeps a logarithm correlation with its original competence. System size may present three kinds of states: monotonic increase, stable, monotonic decrease, and it depends on the quitting threshold of system node and system competitive coefficient. The competence of node will decrease with an exponential or power speed, and in a long time, the competence distribution appears stable which is overlapped by a power law with -1 and original competence distribution. There is a power law or logarithmic correlation between node´s life and its original competence. The number of one node´s competitor will be monotonic increasing logarithmically before its death, and will be proportional to the logarithm of its age. System´s degree distribution obeys an exponential distribution approximately, and it doesn´t depend on the original node competence distribution.