EXACT SOLUTION OF POPULATION REDISTRIBUTIONS IN A MIGRATION MODEL

Authored by Xue-Wen Wang, Li-Jie Zhang, Guo-Hong Yang, Xin-Jian Xu

Date Published: 2013-10

DOI: 10.1142/s0129183113500678

Sponsors: Specialized Research Fund for the Doctoral Program of Higher Education of China

Platforms: No platforms listed

Model Documentation: Other Narrative Mathematical description

Model Code URLs: Model code not found

Abstract

We study a migration model, in which individuals migrate from one community to another. The choices of the source community i and the destination one j are proportional to some power of the population of i (k(i)(alpha)) and j (k(j)(beta)), respectively. Both analytical calculation and numerical simulation show that the population distribution of communities in stationary states is determined by the parameters alpha and beta. The distribution is widely homogeneous with a characteristic size if alpha > beta. Whereas, for alpha < beta, the distribution is highly heterogeneous with the emergence of condensing phenomenon. Between the two regimes, alpha = beta, the distribution gradually shifts from the nonmonotonous (alpha < 0) to scale-free (alpha > 0).

Tags

Migration Zipf's Law nonlinear preference spons