Modeling and Analysis of the Interaction of Neutral, Radical, Undocumented and Welfare Populations: A Competing Species Model

Abstract

The rise of the radical, undocumented and welfare populations throughout the United States has brought concern, debate, and contention to the modern world. The strategies of radicals and undocumented aliens are national and are no longer concentrated in a particular location. In recent papers we have looked at models of the interaction between neutral populations and 1) radical populations, 2) undocumented populations and 3) welfare populations. Individually. These models are unrealistic as all four of these population exist at one time and in one place. In this paper, we present a dynamical model of the interaction between neutral, radical, undocumented and welfare populations simultaneously. The formulation is based on models of interactions between competing species [3] type dynamics. An exploration of the long-term dynamics and stability of homogeneous equilibrium solutions and their stability is given. The paper is given in multiple parts. Part two analyzes the current populations. Part three analyzes the situation when an additional number of radicals are added to the radical population. In sections four and five we analyze a declining undocumented population. In section six and seven we analyze the scenario of a declining welfare population. Sections eight and nine we analyze a reduced population of both undocumented aliens and welfare recipients. Conclusions are presented in section ten.