# User:SxE00/IGEM 2006

## Contents

## Overview of my Contribution to IGEM

I have been an Advisor on Dynamic Systems for the IGEM Imperial College Team. As an advisor I have supervised the study by Imperial IGEM students of ever more complex dynamic systems (from the simple Lotka-Volterra [link] to the complex 2D prey-predator model with bounded growths and killings [link]).

Here is an example of Bifurcation Diagram which was obtained by the team during the various analyses.

## Specific Contributions

- Teaching the Basics of Dynamic Systems

- Generalities

- - What is a Dynamic System?
- - How do you interpret the parameters of a Dynamic System?
- Focus on the Prey-Predator Models

- - What is a Steady Point? Why are so Important?
- - Why do we study the Jacobian to study Dynamic analysis?

- Lecture on Dynamic Systems IGEM:IMPERIAL/2006/Calendar/2006-8-9

- Support for Students

- Support in Mathematics

- - Help for Data Analysis (Methods/Implementation)
- - Help for Calculations in Study of Dynamic Systems

- Creation of Tutorials for IGEM Students (see below) including

- - Templates for Study of Dynamic Systems
- - templates for Presentation of Results

## Tutorials

The following tutorials were prepared to support the work of the Imperial College students participating in IGEM 2006.

**Analysis of a Dynamic System**- Tutorial 1 : Basic Principles of Dynamic Analysis Dynamic Analysis
- Tutorial 2 : Application of Poincare - bendixson Poincare Bendixson
- Tutorial 3 : Template for the Analysis of a Dynamic System Template for Analysis
- Tutorial 4 : Suggestions for the Presentation of Simulation Results Presentation

**Complementary Tutorials**- Tutorial 5 : Curve Fitting with the Least Square Method Least Square Methods
- Tutorial 6 : Solving a Cubic Equation (Cardano's Formulae) Cardano

## Analyses of Dynamic Systems (Scanned Notes)

The final model was complex and depended on 8 independent parameters - 5 after rendering it dimension-less. Cases E=0 and E>0 were separated for practical and theoretical reasons:

- - the case E=0 is a little bit simpler to study (one less parameter)
- - but its study gives good insights into working out the calculations for the general case
- - E=0 and E>0 exhibit some different characteristics as time goes to infinity

Some parts of the analysis involved some complex calculations that were beyond the scope of the project and consequently the students used my results. My notes on the analysis of both cases (E=0) and (E>0) will be scanned soon and posted here for anyone willing to check them