On the Evolution of Nonlinear Density Population Waves in the Socio-Economic Systems

摘要

The most systems in our environment contain components that interact through competition or cooperation, which can lead to system adaptation. Recently, it is especially important to study the behavior of such systems, and to develop and apply new appropriate mathematical methods for studying the processes in these systems. Such approaches have many applications in economy and sociology and are successfully used in mathematics, physics, ecology, biology and technical sciences. In the last decades non-linear models are intensively used to model economic and social systems. In many cases the main features of such complex systems can be explained by a relatively small number of non-linear differential equations. Examples of such systems are some economic organizations. In this paper we model the behavior of a socio-economic system by partial differential equations. The model describes dynamics of populations competing for limited resources. In the model, migration is treated as a advection-diffusion process influenced by changing of the growth rates and the interactions among population individuals. The model describes several novel features of the interacting populations compared to the well-known classic models in population dynamics. Using the modified method of simplest equation and one of its extended versions, we obtain new wave solutions of the model system.