Nonlinear self-organized population dynamics induced by external selective nonlocal processes

Abstract

Highlights It is proposed a model based on non-local operators capable of reproduce several of the equations traditionally used in research on population dynamics, as well as having additional features, useful for describing the phenomenon of pattern formation. The combination of two of the parameters present in the model, namely, α and β , determines the existence of a phase space, characterized by regions with and without patterns. The patterns formed will have M peaks and M valleys, with M ≥ 2. There are ( α, β ) combinations which lead to the formation of degenerate states, where the system seems not to forget its initial conditions. The model allows the study of real systems, such is the case of bacterial populations subjected to inhomogeneous growth conditions. The parameter β represents a macroscopic measure of changes that occur at an individual level in the concentrations of proteins in bacteria, as a product of significant variations in the environment.