Computational and mathematical modelling of plant species interactions in a harsh climate

This thesis will consider the following assumptions which are based on a few insights about the artic climate: (1)the artic climate can be characterised by a growing season called summer and a dormat season called winter (2)in the summer season growing conditions are reasonably favourable and species are more likely to compete for plentiful resources (3)in the winter season there would be no further growth and the plant populations would instead by subjected to fierce weather events such as storms which is more likely to lead to the destruction of some or all of the biomass. Under these assumptions, is it possible to find those change in the environment that might cause mutualism (see section 1.9.2) from competition (see section 1.9.1) to change? The primary aim of this thesis to to provide a prototype simulation of growth of two plant species in the artic that: (1)take account of different models for summer and winter seasons (2)permits the effects of changing climate to be seen on each type of plant species interaction

Stabilizing a mathematical model of plant species interaction

In this paper, we will consider how to stabilize a mathematical model of plant species interaction which is modelled by using Lotka-Volterra system. We first identify the unstable steady states of the system, then we use the feedback control based on the solutions of the Riccati equation to stabilize the linearized system. We further stabilize the nonlinear system by using the feedback controller obtained in the stabilization of the linearized system. We introduce the backward Euler method to approximate the feedback control nonlinear system and obtain the error estimates. Four numerical examples are given which come from the application areas

The Impact of a Time Delay on the Depleted Proportion of the Viral Load of the Virions Due to a Decreased Reproductive Rate of the Infected Cell

While the impact of the variability of the reproductive rate of the infected cell on the viral load of the virions is an on-going research activity, the inclusion of a time delay which mimics the African culture of diverse health inhibiting belief system is a new numerical simulation perspective of solving the mathematical problem and the health policy dimension of HIV/AIDS intervention strategy. The full results of this study which one has not seen elsewhere are presented and discussed in this paper

Analytical Modelling of Steady-State Solutions and its Implication

The interaction between two biological species depends on the process of mathematical modelling. When two plant speciescompete for limited resources, we have used the analytical method to calculate four (4) steady-state solutions which representvalid coexistence two semi-trivial, and a trivial steady-state solution from a first order nonlinear differential equations with theirbiological implications. The full results of this study are presented and discussed

Prediction of the Compressive Strength of Concrete Admixed with Metakaolin Using Gene Expression Programming

One of the problems of optimization of concrete is to formulate a mathematical equation that shows the relationship between the various constituents of concrete and its properties. In this work, modelling of the compressive strength of concrete admixed with metakaolin was carried out using the Gene Expression Programming (GEP) algorithm. The dataset from laboratory experimentation was used for the analysis. The mixture proportions were made of three different water/binder ratios (0.4, 0.5, and 0.6), and the grades of concrete produced were grade M15 and M20. The compressive strength of the concrete was determined after 28 days of curing. The parameters used in the GEP algorithm are the input variables which include cement content, water, metakaolin content, and fine and coarse aggregate, while the response was designated as the compressive strength. The model was trained and tested using the parameters. The R-square value from the GEP algorithm was compared with the use of conventional stepwise regression analysis. With a coefficient of determination (R-square value) of 0.95, the GEP algorithm has shown to be a good alternative for modelling concrete compressive strength