A general growth model for the emergence of power-law distributions

An overwhelming phenomena across natural systems, social systems and ecosystems is discovered in recent years. The phenomena is coined by many terms, such as 1/f noise, Zipf-laws, or scale-free, while power-law distribution of various events or metrics is the fundamental fact that exists in every complex system. It is believed that there exist a mechanism to rule the dynamics of complex system and generate the distribution. In this paper, a general growth model which incorporate Lotka-Volterra dynamics is developed to explain the mechanism of the power-law distribution preliminary. In the model, the influence on power distribution of the spreading rate and the mortality rate can be easily analyzed and explained.