Wyższa Szkoła Zarządzania i Bankowości
LECTURESNOTEBOOKSPACKAGES

3 Population Dynamics


1 Introduction to Simulation and Modeling
2 Discrete Medeling (L-Systems)
3 Population Dynamics
3.1 Fibonacci Growth
3.2 Malthusian Growth
3.3 Logistic Growth
3.4 Phase Trajectories and Limit Cycles
3.5 Lotka-Volterra Predator-Prey Populations
3.6 Gilpins model and transition Chaos
3.7 Additional Exercises
4 Number Representation and Error Propagation
5 Modeling with Random Numbers
6 Heat Transfer in a Rod (Connection Mathematica and C: MathLink)
7 Special Topics in Stochastic Finance
8 Appendix: Introduction to Mathematica
9 Population Dynamics in Vensim®PLE
     
 

3.1 Fibonacci Growth

3.2 Malthusian Growth

3.3 Logistic Growth

3.4 Phase Trajectories and Limit Cycles

3.5 Lotka-Volterra Predator-Prey Populations

3.6 Gilpins model and transition Chaos

3.7 Additional Exercises

Acknowledgements

Parts of the material in this section was taken from a number of sources, which are listed below

Mathematica 4.0, S. Wolfram.
Mathematica User's Guide to the X Front End, Wolfram Research.
Mathematical Modelling and Mathematica, J.E. Cruthirds and L.R. Hitt, Department of Mathematics and Statistics, University of South Alabama, material taken from the Web.
Continuous system modeling, Francois Cellier. Springer Verlag 1991

Introduction

This notebook will introduce some concepts of modelling and simulation of continuous systems. Emphasis is on examples taken from nature. We will use inductive instead of deductive reasoning, meaning that our models are not created on the basis of physical understanding of the processes we wish to capture: We rather make some observations about the system under study an then try to fit  a (meta) model to the observed data.

You will notice that this notebook contains material covering Population & Growth modelling and simulation of these phenomena using Mathematica. In the text  you will  find a large number of exercises that will help to understand the material.  Furthermore, at the end of the notebook you will  find three additional exercises.

Important  instructions  for  all students:
Each notebook  contains several questions that must be handed in. Theses questions are labeled accordingly:

Required: These questions must be done by all students.

Advanced:  These questions are considered to be more difficult and may be assigned by the instructor.

Optional:   These questions are optional  to all students  and will be counted towards   extra  marks.


 
     
  Lectures | Notebooks | Packages

 
  Copyright © 2003 Wyższa Szkoła Zarządzania i Bankowości. Wszystkie prawa zastrzeżone
webmaster@wszib.edu.pl