System analysis and simulations

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The system was studied analytically and numerically. Both studies showed an unexpected structural stability property in the parameter range of physical interest. Indeed, we get an analytic expression for the Jacobian matrix (a diagonal matrix) whose determinant becomes 0 only if almost one of basical diluition factor becomes 0. After a careful study we found the reason of this behavior in the modeling process, particularly in the use of the second assumption. Matlab, Mathematica and Matcont were used to complete the study with simulations and bifurcation diagrams that confirmed the previous analytic study.
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The system was studied analytically and numerically. Both studies showed an unexpected structural stability property in the parameter range of physical interest. Matlab, Mathematica and Matcont were used to complete the study with simulations and bifurcation diagrams that confirmed the previous analytic study.
[[Click here]] to see the bifurcation diagram of [PHO8], an output of the system.  
[[Click here]] to see the bifurcation diagram of [PHO8], an output of the system.  
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Once we get the steady state behavior of the outputs separately, we have to choose some ''index'' for the performances of the system. The ratio between the two outputs, i.e. PHO8/PHO8085, appears to be appropriated for our purpose. [[Click here to see PHO8/PHO8085]] at the varying of system parameters.
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Once we computed the steady state behavior of the outputs (Pho4 and Pho80Pho85) separately, we have to choose some ''index'' for the performances of the system. The ratio between the two outputs, i.e. PHO8/PHO8085, appears to be appropriated for our purpose. [[Click here to see PHO8/PHO8085]] at the varying of system parameters.
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In order to model oleic acid we used SA and SB as inputs as functions of oleic acid concentration (o.a.), i.e. SA(o.a.), SB(o.a.). [[Click here to see them]].
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In our last analysis we want to ''put oleic acid into the model'': notice that the model used upfront has SA and SB as input and they are independent from the oleic acid concentration. Now we want to study the behavior of the system using SA and SB as functions of oleic acid concentration (o.a.), i.e. SA(o.a.), SB(o.a.). [[Click here to see them]].
 
Using these input functions, we can get the steady state behavior when o.a. varies for different parameter values.  
Using these input functions, we can get the steady state behavior when o.a. varies for different parameter values.  
[[Click here for the results]]
[[Click here for the results]]
To get informations about the transient response of the system and to ''test'' the detected parameters we used a new Matlab file which simply simulates the system. The results are presented [[here]].
To get informations about the transient response of the system and to ''test'' the detected parameters we used a new Matlab file which simply simulates the system. The results are presented [[here]].

Latest revision as of 11:33, 23 October 2007

The system was studied analytically and numerically. Both studies showed an unexpected structural stability property in the parameter range of physical interest. Matlab, Mathematica and Matcont were used to complete the study with simulations and bifurcation diagrams that confirmed the previous analytic study. Click here to see the bifurcation diagram of [PHO8], an output of the system. Once we computed the steady state behavior of the outputs (Pho4 and Pho80Pho85) separately, we have to choose some index for the performances of the system. The ratio between the two outputs, i.e. PHO8/PHO8085, appears to be appropriated for our purpose. Click here to see PHO8/PHO8085 at the varying of system parameters.

In order to model oleic acid we used SA and SB as inputs as functions of oleic acid concentration (o.a.), i.e. SA(o.a.), SB(o.a.). Click here to see them.

Using these input functions, we can get the steady state behavior when o.a. varies for different parameter values. Click here for the results

To get informations about the transient response of the system and to test the detected parameters we used a new Matlab file which simply simulates the system. The results are presented here.

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