A mathematical-model approach to human population explosions caused by migration

作者：Tabata Minoru^*; Eshima Nobuoki; Takagi Ichiro

来源：Nonlinear Analysis: Real World Applications , 2010, 11(5): 4027-4042.

DOI：10.1016/j.nonrwa.2010.03.009

• Population explosion
• Master equation
• Nonlinear integro-partial differential equation
• Blow-up solution
• Human population dynamics

If the human population density becomes extremely high in a small area, then we say that a population explosion occurs in the area. Geographical movements of human population can form a regional overconcentration of population. If such an overconcentration becomes excessive, then it often forms a population explosion. In this paper, by taking a mathematical-model approach to human population explosions caused by migration, we obtain a sufficient condition for population to explode. It is known in sociodynamics that geographical population movements are described by a nonlinear integro-partial differential equation whose unknown function denotes the population density. This equation is called the master equation, and has its origin in statistical physics. We express a population explosion as a blow-up solution to the initial-value problem for this equation. We will study a population explosion as an interdisciplinary subject among human population dynamics, statistical physics, and the theory of nonlinear functional equations. The principal result is as follows: if a human population migrates within a sufficiently small domain, if the gradient of initial population density is sufficiently large, if the population gravitates strongly toward densely populated areas, and if a cost incurred in moving is sufficiently small, then a population explosion occurs.

• 出版日期2010-10