System analysis and simulations
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.