| dc.description.abstract | We begin in chapter I with literature review, which gives a brief background on
Waterhyacinth We look at the growth and reproduction, distribution, control methods, and
problems caused by water hyacinth. We also give a statement of the problem, objectives,
methods used in carrying out the project and conclude the chapter by giving a justification. In
chapter 2 we derive a model that describes the population of water hyacinth. In section 22,
the dynamics of environmental carrying capacity (nutrient concentration) are incorporated in
this model. 111 section 2.3 we nondimensionalize our model in order to reduce the numbers
of parameters. This also helps us to group the parameters in a meaningful way.
In chapter 3 we seek to establish the long term behaviour of the system by describing a
procedure for the qualitative analysis of water hyacinth and nutrient concentration. This
consists of separating the state variables into fast and slow categories In section 3. I the
dynamics of the fast variables are analysed first while holding the slow variables fixed
Then, in section 3.2 the dynamics of the slow variables and fast variables are analysed
simultaneously.
In the full analysis of the model, we consider the possible dynamical regimes depending
on the parameters. These could be stable or unstable solutions, periodic oscillations and a
limit cycle. In chapter 4 we examine how the nature of the system will vary when we assign
various numerical values to the population parameters, namely the intrinsic growth rate and
nutrient concentraticn
We conclude in chapter "5with some remarks concerning too biological interpretations of
the results obtained in chapter 3 and 4 | en |
