IGEM:IMPERIAL/2006/project/Oscillator/Modelling/Analysis

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MODELLING THE OSCILLATOR AND ITS COMPONENTS:



Analysis report of the past progress --31/07/06


Back to simplicity -- another new matlab programme has been done, we just used ode23 to solve LV differential equations
-- click here for the first report --02/08/06
-- click here for the second report --04/08/06
-- click here for the third report --07/08/06
-- click here for the fourth report --07/08/06
-- click here for the fifth report --10/08/06
-- click here for the sixth report --10/08/06


Jacobian anaylsis of stationary point for stability of oscillation. click here --04/08/06


Introduction to analysis of the 2-D ODEs. click here --14/08/06
--revised version 1 click here --21/08/06


Study and Characterisation of a limit cycle. click here --06/09/06


Stability analysis of modified Lotka-Volterra systems
-- Version 1, production of the prey is modelled by pseudo Michaelis-Menten kinetics click here --16/08/06
-- Version 2, productions of the prey and predator are modelled by pseudo MM kinetics click here --21/08/06
-- Version 3, production and death of the prey is modelled by pseudo MM kinetics click here --06/09/06
-- Version 4, Comination of Version 1 2 3 click here --06/09/06


Further Study of the complicated modelling of Version 4

Specail thanks to Matthieu Bultelle for all the mathematical analysis of this model! 

-- Trial 1, by defining R=B*C/D to simplify stability analysis, click here for analysis and click here for appendix of full-size graphs --06/09/06
-- Trial 2, interesting cases of trial 1, click here for cases of R=1 and click here for an interesting nice limit cycle --06/09/06
-- Trial 3, by re-defining R=C/D for better system analysis click here for analysis and click here for appendix of full-size graphs --07/09/06


List of templates designed by Matthieu Bultelle:
-- Part 1, Dynamic Analysis of a system, click here
-- Part 2, Poincare Analysis for limit cycle, click here
-- Part 3, Theoretical Model Analysis, click here
-- Part 4, Presentation of Results, click here


Template for analysing dynamical system : IGEM:IMPERIAL/2006/project/modelling_template


A powerful Java Applet

Molecular Prey-Predator-System

Molecular Prey-Predator using JOde

a=1;a0=1;b=5;b0=0.5;c=0.01;c0=1;d=0.02;e=0.0 Instructions on using the JOde Applet

Using the applet written by: Marek Rychlik

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