Team:WHU-China/Project/Modeling

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  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is the Hopf bifurcation point , when&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  ,it is able to generate a stable periodic solution.
  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is the Hopf bifurcation point , when&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;  ,it is able to generate a stable periodic solution.
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Revision as of 08:02, 1 October 2011

In the mathematic modeling section , we make stimulation about the oscillator and consider two possible circumstance.
The system including two protein:
Using differential equation to describe the system:
Where      means the volume of      ,      means the volume of      ,      means the delay time of the reaction.
This is the classic delay ODE , using the matlab software, we got the solution image ;
We mainly consider the system including three protein: We also use delay ODE to describe the system:
where:         means the volume of     
though dimensionless:
The balance point of the equation is                  and       

Using the MATLAB software to plot we got the solution image:

Bifurcation analysis chart:
           is the Hopf bifurcation point , when         ,it is able to generate a stable periodic solution.
           is the Hopf bifurcation point , when            ,it is able to generate a stable periodic solution.
           is the Hopf bifurcation point , when            ,it is able to generate a stable periodic solution.
           is the Hopf bifurcation point , when            ,it is able to generate a stable periodic solution.

Cycle with the curve of each parameter:

As the changes of cycle time with the change of the parameters in the image , we can get the conclusion that:
     1.      have little influence on the range.
     2.      do not have much influence on the cycle time.
     3.      have inversely proportional relationship with the cycle time , it have a huge influence on the cycle      time , but little impact on the range (Can be used to adjust the cycle to maintain constant amplitude)
     4. When      , have little influence on the range.
This conclusion we get before can be used to guide the design of biological systems, in order to achieve the adjustment period, amplitude can adjust the size of some parameters.

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