A Discrete – Time Mathematical Model for Homogeneous Population Density Dynamics of Single Weed Species

Abstract

In this paper, the biological process is utilized to formulate a discrete-time homogeneous model for the dynamics of weed population density. Steady state solutions were obtained and analyzed them for local and global stabilities. The results revealed that our model is locally asymptotically stable but globally unstable. This result is contrary to the interesting property of the most standard biological one-dimensional discrete models, which display global stability if they are locally stable.  Although, our model equation falls within the category of population models that exhibit local stability but globally not stable. It is concluded that, the weed population may exhibit unexpected behaviours.

Keywords: Biological process, Discrete-time model, Local stability, Global stability, Population density