Interaction of human migration and wealth distribution

Abstract

a b s t r a c tDynamics of human populations depends on various economical and social factors. Their migration is partially determined by the economical conditions and it can also influence these conditions. This work is devoted to the analysis of the interaction of human migration and wealth distribution. The model consists of a system of equations for the population density and for the wealth distribution with conventional diffusion terms and with cross diffusion terms describing human migration determined by the wealth gradient and wealth flux determined by human migration. Wealth production and consumption depend on the population density while the natality and mortality rates depend on the level of wealth. In the absence of cross diffusion terms, dynamics of solutions is described by travelling wave solutions of the corresponding reaction-diffusion systems of equations. We show persistence of such solutions for sufficiently small cross diffusion coefficients. This result is based on the perturbation methods and on the spectral properties of the linearized operators.

Soft Randomized Machine Learning Procedure for Modeling Dynamic Interaction of Regional Systems

“…The proof is postponed to the Appendix A. Therefore, the randomized dynamic model in Equations (7)- (11) includes three random parameters b = {b 1 , b 2 , b 3 } of the interval type that are defined over the three-dimensional cube with faces (Equations (12) and 13), i.e.,…”

“…Note that the problem of migration touches upon many aspects of socioeconomic, psychological and political status of the space of migratory movements. Thus, of crucial role is the structural analysis of inter-and intraregional migration flows [4] and motivations that generate them [2,11]. The results of structural and motivational analysis of migratory processes are used for computer simulation.…”

Equilibrium and Stability of Entropy Operator Model for Migratory Interaction of Regional Systems

“…Note that the problem of migration touches upon many aspects of socioeconomic, psychological and political status of the space of migratory movements. So of crucial role is the structural analysis of inter-and intraregional migration flows [6] and motivations that generate them [7,8]. The results of structural and motivational analysis of migratory processes are used for computer simulation.…”

Preface

“…A. MOROZOV [22]. Zincenko et al predict scenarios of a sharp population decline and deterioration of the economic situation after some periods of intensive transient growth.…”

“…The importance of the shape of the functional response in ecological predator-prey models has been previously emphasized [3,6,15]. For example, recent studies revealed the role of herd behaviour and collective defence of animals in dynamics of predator-prey systems: animal aggregation of individuals in herds would reduce their consumption by predators and this can be mathematically described via a square root functional response [22]. In their article, Vilches et al comprehensively explore a predator-prey model with a generic square root functional response [21].…”