A NONLINEAR ANALYSIS OF THE DEPLETION OF A FERTILE TOPSOIL DUE TO

INCREASING VEGETATION COVER AND RAINFALL PRESSURE

Sarki D.S., Pam B.D., Bwirdimma D.G and Sarki B.D.

Department of Mathematics, Federal College of Education Pankshin, Plateau State, Nigeria

Department of Computer Sciences, Federal College of Education Pankshin, Plateau State, Nigeria

Department of Science and Technology, Faculty of Education, University of Jos, Plateau State, Nigeria

Abstract

This paper describes dual impact of a continues mineral uptake by a growing

vegetation biomass and an increasing rainfall stress on a fertile topsoil. The study

identifies four mutually existing but interdependent interacting ecological

components comprising of, in the first category, vapour, cloud droplets and raindrops

phases, the humid phase (hot air), the fertile topsoil and the component of vegetation

biomass. It is further assumed that while the density of vegetation cover exhibits a

logistic type growth, the other phases undergo ecological type growth and nonlinear

interactions. The stability theory of differential equations and numerical simulation

were used to establish the stability behaviours of the proposed model. It is shown that

the depletion of fertile topsoil could be due to the continues mineral uptake by

vegetation cover and the increasing stress of rain drop