IGEM:IMPERIAL/2006/project/Oscillator/Theoretical Analyses/Results

From OpenWetWare
Jump to navigationJump to search

Analysis of the Model of the Molecular Predation Oscillator


Our Results

During the run of the summer 2006, we had time to study six 2-dimensional Dynamical Systems. Unfortunately we lacked time to carry out a thorough analysis of the 3D model.In order of complexity, the 2D models are:



  • 2D Model 1: Lotka – Volterra
Model1.PNG
  • Lotka-Volterra is the first (and most famous) model for prey-predator interactions and is notoriously endowed with some very appealing properties. Lotka-Volterra also was a major inspiration for the design of the molecular predation oscillator.



  • 2D Model 2: Bounded Prey Growth
Model2.PNG



  • 2D Model 3: Bounded Predator and Prey Growth
Model3.PNG
  • Bounding the growth of the preys only stabilises the system to the extent we cannot make it oscillate anymore.
  • We now seek ways to obtain oscillations by bounding the growth terms of both preys and predators.
  • Detailed Analysis for Model with Bounded Growths



The path from Lotka-Volterra to the 2D model of the Predation Oscillator


  • 2D Model 3bis: Bounded Prey Growth and Prey Killing
Model3a.PNG



  • 2D Model 4: Bounded Predator and Prey Growth with Controlled Killing of Preys
Model4.PNG
  • Bounding growth and killing yielded oscillations; bounding prey and predator growths did not.
  • We now combine both previous models and get one step closer to the final system
  • Detailed Analysis for Model 4



  • Final 2D Model : 2D Model 5
Model5.PNG
  • Model 4 can be made to oscillate but also exhibits some very unrealistic properties.
  • Fortunately experimental conditions lead us to introduce a final dissipative term –eU to the derivative of the prey population.
  • We investigate the properties of this final 2D model and prove that the new dissipative term confers it some very interesting characteristics.
  • Detailed Analysis of the complete 2D Model

<html> <!-- Start of StatCounter Code --> <script type="text/javascript" language="javascript"> var sc_project=1999441; var sc_invisible=1; var sc_partition=18; var sc_security="18996820"; </script>

<script type="text/javascript" language="javascript" src="http://www.statcounter.com/counter/frames.js"></script><noscript><a href="http://www.statcounter.com/" target="_blank"><img src="http://c19.statcounter.com/counter.php?sc_project=1999441&amp;java=0&amp;security=18996820&amp;invisible=1" alt="website statistics" border="0"></a> </noscript> <!-- End of StatCounter Code --> </html>