Multistability analysis of a nutrient-dependent model system for water hyacinth

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