+234 813 0686 500
+234 809 3423 853
info@grossarchive.com

# CRITICAL ANALYSES OF THE DISCRETE LOGISTIC MODEL AND STRUCTURED POPULATIONS

• Chapters:4
• Pages:54
• Methodology:Scientific Method
• Reference:NO
• Format:Microsoft Word
(Mathematics)
CRITICAL ANALYSES OF THE DISCRETE LOGISTIC MODEL AND STRUCTURED POPULATIONS
1.0      INTRODUCTION
1.1      Introduction and Motivation
1.2      Aims and objective
1.3      Statement of the problem
1.4      Scope of the study
1.5      Definition of terms
2.0      CHAPTER TWO: LITERATURE REVIEW
2.1      Models and Modelling
2.2      TheLogistic model
2.3      The logistic differential equation
2.4      The logistic function
2.5      The logistic graph/map
2.6      Comparison of the discrete and continuous models
CHAPTER THREE
3.0      The discrete logistic models
3.1      Structured Population models
CHAPTER FOUR: PROBLEMS AND SIMULATION
4.0      Data simulation and
4.1      Behaviour of the model
4.2      Graphing the model
Chapter one
INTRODUCTION
The well-known logistic differential equation was originally proposed by the Belgian mathematician Pierre-François Verhulst (1804–1849) in 1838, in order to describe the growth of a populationunder the assumptions that the rate of growth of the population was proportional to the existing population and the amount of available resources.
When this scenario is "translated" into mathematics, it results to the differential equation where t denotes time, P0 is the initial population, and r, k are constants associated with the growth rate and the carrying capacity of the population
Although, it can be considered as a simple differential equation, in the sense that it is completely solvable by use of elementary techniques of the theory of differential equations, it has tremendous and numerous applications in various fields. The first application was already mentioned, and it is connected with population problems, and more generally, problems in ecology. Other applications appear in problems of chemistry, linguistics, medicine (especially in modelling the growth of tumors), pharmacology (especially in the production of antibiotic medicines), epidemiology, atmospheric pollution, flow in a river, and so forth.
Nowadays, the logistic differential equation can be found in many biology textbooks and can be considered as a cornerstone of ecology. However, it has also received much criticism by several ecologists.
However, as it often happens in applications, when modelling a realistic problem, one may decide to describe the problem in terms of differential equations or in terms of difference equations. Thus, the initial value problem which describes the population problem studied by Verhulst, could be formulated instead as an initial value problem of a difference equation. Also, there is a great literature on topics regarding discrete analogues of the differential calculus. In this context, the general difference equation has been known as the discrete logistic equation and it serves as an analogue to the initial value problem.
There are several ways to "end up" with (ii) starting (i) from or and some are:
•         by iterating the function,F(x) = µX(1 - X),  ,  which gives rise to the difference equation Xn+1 = µXn(1 - Xn)
•         by discretizing using a forward difference scheme for the derivative, which gives rise to the difference equation where  ,  being the step size of the scheme, or
•         by "translating" the population problem studied by Verhulst in terms of differences: if Pn is the population under study at time  , its growth is indicated by  . Thus, the following initial value problem appears:
Notice of course that all three equations are special cases of (i)
AIMS AND OBECTIVES
Thisstudy is being conducted to critically analyse the Discrete Logistic model and structured populations.At the end of the study; we should be able to
?         Analyse logistic models under different circumstances and values of the rate of population growth.
?         Solve some problems involving the application of the Discrete logistic model to real life situations and draw conclusions from the solutions of such
?         Construct models for some structured populations and their behaviours
?         Solve problems relating the structured populations to real life situations.

#### Project Details

 Department Mathematics Project ID MTH0004 Price ₦3,000 (\$9) Chapters 4 Chapters No of Pages 54 Pages Methodology Scientific Method Reference NO Format Microsoft Word

#### Project Details

 Department Mathematics Project ID MTH0004 Price ₦3,000 (\$9) Chapters 4 Chapters No of Pages 54 Pages Methodology Scientific Method Reference NO Format Microsoft Word

#### Related Project Topics

ABSTRACT So important is the need to display the products of the art school in IMT. As there is need for showcasing, so there is need for proper preservation and conservation of these works. This urge for an art gallery in the IMT art school has... Continue Reading
. CHAPTER ONE 1.0 INTRODUCTION 1.1 Background of the Study Tuberculosis or TB (short for Tubercles Bacillus) is an air borne and highly infectious disease caused by infection with the bacteria mycobacterium tuberculosis. An... Continue Reading
• Type:Project
• ID:MTH0003
• Department:Mathematics
• Pages:60
• Chapters:5
• Methodology:Scientific Method
• Reference:YES
ABSTRACT The precise content of this project was to construct a model shell and tube heat exchanger. The material for construction of this project (equipment) and their dimensions are as follows: 500mm length of a tube bundle 20mm diameter of... Continue Reading
ABSTRACT This paper examines the spread and control of Avian Influenza. A non-linear mathematical model for the problem is formulated and analyzed. For the prevalence of the disease and the ease of analysis, the model was... Continue Reading
• Type:Project
• ID:MTH0006
• Department:Mathematics
• Pages:65
• Chapters:5
• Methodology:Scientific Method
• Reference:YES
ABSTRACT In this project, I presented a nonlinear mathematical model for the spread of Polio in a population with variable size structure including the role of vaccination. Using an expanded SIR model, the present... Continue Reading
• Type:Project
• ID:MTH0005
• Department:Mathematics
• Pages:60
• Chapters:5
• Methodology:Scientific Method
• Reference:YES
ABSTRACT All commercial application developed (irrespective of the programming environment used) are to business models. Applications help to computerize business models. It is the computerization... Continue Reading
• Type:Project
• ID:CPU0204
• Department:Computer Science
• Pages:62
• Chapters:5
• Methodology:simple percentage
• Reference:YES
ABSTRACT This study investigated the challenges of secretaries in model financial houses. The theoretical frame work for this study was provided by the review of related literature.... Continue Reading
ABSTRACT The development of accounting systems and the computerization of these systems in a small scale business environment is... Continue Reading
• Type:Project
• ID:ACC0224
• Department:Accounting
• Pages:118
• Chapters:5
• Methodology:Descriptive
• Reference:YES
ABSTRACT Generally, where a court is faced with the problem of determining a suit before it, such can only be solved after making an enquiry into the relevant facts of the evidence put before it by the parties, drawing inferences from those facts, and... Continue Reading
• Type:Project
• ID:LAW0004
• Department:Law
• Pages:54
• Chapters:5
• Methodology:Primary data
• Reference:YES
The electoral process is a total process that includes registration of voters, identifying the political parties to be voted for, voting, counting of votes, and declaration of election results. This process is the foundation of civil societies. A... Continue Reading
• Type:Project
• ID:LAW0008
• Department:Law
• Pages:95
• Chapters:5
• Methodology:Secondary data
• Reference:YES