Human behaviors are usually determined by some social and/or economic trend. In the past few years, many attempts have been made, in the field of complex scientific systems, to describe the dynamics of these behaviors quantitatively and have an accurate understanding of the corresponding mechanisms. In this paper, a generalized potential, that is, a migration desire function defined by the age of the migrating people, the migrating distance, and the so-called economic-population density of the emigration area, is proposed. It can be transformed into Hamilton-Jacobi equation by using a random dynamical method, Langevin equation, so that the decision-making behavior can be investigated, based on a statistic framework during a group migration process. By taking use of the multi-dimensional steepest descent method, the Hamilton-Jacobi equation is solved; the solution shows that the information entropy of the system varies, leading by a single peak, as the age of the migrating people increases. It also demonstrates that the second derivative of the migrating distance to the information entropy has a change of zero-crossing (which actually means a phase change). The third characteristic of the solution is that the information entropy follows another single peak as the economic-population density increases. A deeper analysis reveals the significance behind these findings and the corresponding mechanisms. So some new understandings of the group human behaviors can be obtained, and some worthy references can be provided for some related administrative offices.