Defining a system in MatCont where a parameter depends on other parameter value












0












$begingroup$


I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way



if (TS <= 1.375){                                                         

    UU = 0.02938*TS^3 - 0.006729*TS^2 + 0.05514*TS + 0.0004823;              

}                                                                         

if (1.375 < TS && TS <= 7){                                               

    UU = 0.01138*TS^3 - 0.06751*TS^2 + 0.203*TS - 0.05441;                   

}                                                                         

if (TS > 7){                                                              

    UU = -0.0012*TS^3 + 0.048*TS^2 + 0.42*TS - 2.9;                          

}


So far I've defined the system in the following way



RR'= BetaRStar*(Rt-CTR-CDR) - KaT*TT*RR + KdT*CTR - KaD*DD*RR + KdD*CDR-BetaR*RR

TT'=UU - KaT*TT*RR + KdT*CTR - alpha*Kcat*TT/(KM + TT) - BetaT*TT               

DD'=alpha*Kcat*TT/(KM + TT) - KaD*DD*RR + KdD*CDR-BetaD*DD                      

CTR'=KaT*TT*RR - KdT*CTR                                                        

CDR'=KaD*DD*RR - KdD*CDR


I don't have any idea on how i should define $UU$. Thanks for your help.






systems-of-equations biology bifurcation







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  • $begingroup$
    Unfortunatly in the system window definition i can't insert if statement or amy other function.
    $endgroup$
    – Federico Bertacco
    Dec 9 '18 at 13:33
















0












$begingroup$


I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way



if (TS <= 1.375){                                                         

    UU = 0.02938*TS^3 - 0.006729*TS^2 + 0.05514*TS + 0.0004823;              

}                                                                         

if (1.375 < TS && TS <= 7){                                               

    UU = 0.01138*TS^3 - 0.06751*TS^2 + 0.203*TS - 0.05441;                   

}                                                                         

if (TS > 7){                                                              

    UU = -0.0012*TS^3 + 0.048*TS^2 + 0.42*TS - 2.9;                          

}


So far I've defined the system in the following way



RR'= BetaRStar*(Rt-CTR-CDR) - KaT*TT*RR + KdT*CTR - KaD*DD*RR + KdD*CDR-BetaR*RR

TT'=UU - KaT*TT*RR + KdT*CTR - alpha*Kcat*TT/(KM + TT) - BetaT*TT               

DD'=alpha*Kcat*TT/(KM + TT) - KaD*DD*RR + KdD*CDR-BetaD*DD                      

CTR'=KaT*TT*RR - KdT*CTR                                                        

CDR'=KaD*DD*RR - KdD*CDR


I don't have any idea on how i should define $UU$. Thanks for your help.






systems-of-equations biology bifurcation







share|cite|improve this question









$endgroup$












  • $begingroup$
    Unfortunatly in the system window definition i can't insert if statement or amy other function.
    $endgroup$
    – Federico Bertacco
    Dec 9 '18 at 13:33














0












0








0





$begingroup$


I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way



if (TS <= 1.375){                                                         

    UU = 0.02938*TS^3 - 0.006729*TS^2 + 0.05514*TS + 0.0004823;              

}                                                                         

if (1.375 < TS && TS <= 7){                                               

    UU = 0.01138*TS^3 - 0.06751*TS^2 + 0.203*TS - 0.05441;                   

}                                                                         

if (TS > 7){                                                              

    UU = -0.0012*TS^3 + 0.048*TS^2 + 0.42*TS - 2.9;                          

}


So far I've defined the system in the following way



RR'= BetaRStar*(Rt-CTR-CDR) - KaT*TT*RR + KdT*CTR - KaD*DD*RR + KdD*CDR-BetaR*RR

TT'=UU - KaT*TT*RR + KdT*CTR - alpha*Kcat*TT/(KM + TT) - BetaT*TT               

DD'=alpha*Kcat*TT/(KM + TT) - KaD*DD*RR + KdD*CDR-BetaD*DD                      

CTR'=KaT*TT*RR - KdT*CTR                                                        

CDR'=KaD*DD*RR - KdD*CDR


I don't have any idea on how i should define $UU$. Thanks for your help.






systems-of-equations biology bifurcation







share|cite|improve this question









$endgroup$




I'm trying to define a biological system in MatCont but I'm facing the following problem. A parameter $UU$ depends on another parameter $T_S$ in the following way



if (TS <= 1.375){                                                         

    UU = 0.02938*TS^3 - 0.006729*TS^2 + 0.05514*TS + 0.0004823;              

}                                                                         

if (1.375 < TS && TS <= 7){                                               

    UU = 0.01138*TS^3 - 0.06751*TS^2 + 0.203*TS - 0.05441;                   

}                                                                         

if (TS > 7){                                                              

    UU = -0.0012*TS^3 + 0.048*TS^2 + 0.42*TS - 2.9;                          

}


So far I've defined the system in the following way



RR'= BetaRStar*(Rt-CTR-CDR) - KaT*TT*RR + KdT*CTR - KaD*DD*RR + KdD*CDR-BetaR*RR

TT'=UU - KaT*TT*RR + KdT*CTR - alpha*Kcat*TT/(KM + TT) - BetaT*TT               

DD'=alpha*Kcat*TT/(KM + TT) - KaD*DD*RR + KdD*CDR-BetaD*DD                      

CTR'=KaT*TT*RR - KdT*CTR                                                        

CDR'=KaD*DD*RR - KdD*CDR


I don't have any idea on how i should define $UU$. Thanks for your help.






systems-of-equations biology bifurcation




systems-of-equations biology bifurcation






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share|cite|improve this question











share|cite|improve this question




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asked Dec 9 '18 at 8:31









Federico BertaccoFederico Bertacco

11




11












  • $begingroup$
    Unfortunatly in the system window definition i can't insert if statement or amy other function.
    $endgroup$
    – Federico Bertacco
    Dec 9 '18 at 13:33


















  • $begingroup$
    Unfortunatly in the system window definition i can't insert if statement or amy other function.
    $endgroup$
    – Federico Bertacco
    Dec 9 '18 at 13:33
















$begingroup$
Unfortunatly in the system window definition i can't insert if statement or amy other function.
$endgroup$
– Federico Bertacco
Dec 9 '18 at 13:33




$begingroup$
Unfortunatly in the system window definition i can't insert if statement or amy other function.
$endgroup$
– Federico Bertacco
Dec 9 '18 at 13:33










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