A mathematical model for global population growth

World population growth is perceived as the main global problem now dominated by the population explosion. In describing this process statistics and demography by pursuing the standard approach in forecasting world population indicate that in the next 100–150 years the world population may level off at $12\cdot10^9$ people as one of the possible scenarios due to the decrease in fertility in the III World. In developing an alternative approach one can consider the world population as a dynamic system and apply to the description of growth concepts and methods developed in systems analysis and many-particle physics. The phenomenological theory describes the population growth as a self-similar process. The population transformation is seen as a stabilized explosive instability, leading to a world population of $15\cdot10^9$. The extension of the model provides an estimate of the time of the origin of the humankind $T_0\sim4$ Myrs ago and of the number of people who ever lived $M\sim100\cdot10^9$. In the following treatment world population will be seen as an open system and its growth to great extent independend of external factors in development.