Authors : Nasir M. Olalekan and Ibinayin S. Jerom
Abstract: In this study, researchers employed the biological process to formulate a discrete-time homogeneous model for the dynamics of weed density interaction through biologically defined states and the mechanism of seedling recruitment incorporating weed reproduction from persistent seed bank within a crop growing season. Researchers obtained its steady-state solutions and analyzed them for local and global stabilities. Researchers discovered that the 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, the model equation falls within the category of population models that exhibit local stability but not globally stable. However, researchers conclude that the weed population may exhibit unexpected behaviours that is the population may not be predictable.
Nasir M. Olalekan and Ibinayin S. Jerom, 2013. A Discrete Mathematical Model for Homogeneous Population Density Dynamics of Single Weed Species. Journal of Modern Mathematics and Statistics, 7: 72-76.