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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

<html> <HEAD> <TITLE>Molecular Prey-Predator-System</TITLE>

       <LINK REL="stylesheet" TYPE="text/css" HREF="style.css">

</HEAD> <BODY> <H1>Molecular Prey-Predator using JOde</H1> <P><!-- Insert HTML here --><APPLET code="com/rychlik/jode/JOdeApplet.class" NAME="JOde" width=650 height=750 archive="http://openwetware.org/images/a/a3/JOdeApplet.jar" mayscript="true"> <PARAM NAME="isframed" VALUE="false"> <PARAM NAME="background" VALUE="c0c0c0"> <PARAM NAME="autonomous" VALUE="true"> <PARAM NAME="min1" VALUE="0"> <PARAM NAME="max1" VALUE="50"> <PARAM NAME="min2" VALUE="0"> <PARAM NAME="max2" VALUE="1"> <PARAM NAME="variable0" VALUE="t"> <PARAM NAME="equation0" VALUE="a=1;a0=1;b=5;b0=0.5;c=0.01;c0=1;d=0.02;e=0.01"> <PARAM NAME="variable1" VALUE="X"> <PARAM NAME="variable2" VALUE="Y"> <PARAM NAME="equation1" VALUE="a*X/(a0+X)-b*X*Y/(b0+X)-e*X"> <PARAM NAME="equation2" VALUE="c*X*Y/(c0+X*Y)-d*Y">

       <PARAM NAME="initconds" VALUE="40,1;10,0.2">

<PARAM NAME="showinitconditions" VALUE="true"> <PARAM NAME="showpoints" VALUE="false"> <PARAM NAME="showslopes" VALUE="true"> <PARAM NAME="showaxes" VALUE="true"> <PARAM NAME="minparameter" VALUE="0"> <PARAM NAME="maxparameter" VALUE="2000"> <PARAM NAME="parametersegments" VALUE="20000"> <PARAM NAME="algorithm" VALUE="RK4"> <PARAM NAME="label" VALUE="Molecular Prey-Predator"> </APPLET> </P>


Instructions on using the JOde Applet</A></EM></P> <P>Using the applet written by: <A HREF="http://alamos.math.arizona.edu/">Marek Rychlik</A> </BODY> </html>