(* Generated by JWS Online *)

(* This is an experimental feature of JWS Online. Please report any mistakes.*)

(* Note that the following notable SBML entities or features are not supported in notebook outputyet: *)
    (* Events *)
    (* Constraints *)
    (* Units and UnitDefinitions *)
    (* AlgebraicRules *)
    (* conversionFactors *)

variables = {
Y[t], Z[t]
};

initialValues = {
Y[0] == 0.0, Z[0] == 0.0
};

rates = {
r1, r2, r3, r4
};

rateEquations = {
r1 -> F[X, r1\[LetterSpace]Ty], r2 -> r2\[LetterSpace]a*Y[t], r3 -> F[X, r3\[LetterSpace]Ty]*F[Y[t], r3\[LetterSpace]Tz], r4 -> r4\[LetterSpace]a*Z[t]
};

parameters = {
X -> 0.0, r1\[LetterSpace]Ty -> 0.5, r2\[LetterSpace]a -> 1.0, r3\[LetterSpace]Ty -> 0.5, r3\[LetterSpace]Tz -> 0.5, r4\[LetterSpace]a -> 1.0, cell -> 1.0
};

assignments = {
F[X_,T_] -> Piecewise[{{1, X >= T}}, 0]
};

events = {

};

speciesAnnotations = {

};

reactionAnnotations = {

};

units = {
{"time" -> "", "metabolite" -> "", "extent" -> ""}
};

(* Time evolution *)
odes = {
Y'[t] == 1.0*r1 -1.0*r2, Z'[t] == 1.0*r3 -1.0*r4
};
timeCourse = NDSolve[Join[odes, initialValues]//.rateEquations//.assignments//.parameters, variables, {t, 0, 100}];

(* Steady-state solution initialized with result of time evolution *)
findRootEquations = odes /.D[_[t],t]->0;
findRootVariables = Partition[Flatten[{#, #/.timeCourse/.t->100} &/@variables],2];
steadyStateVariables = FindRoot[findRootEquations//.rateEquations//.assignments//.parameters, findRootVariables, MaxIterations->100]
fluxes = #//.assignments//.parameters/.steadyStateVariables&/@rateEquations

(* Plot the time evolution of the variables *)
plotTable=Table[Plot[variables[[i]]/.parameters/.timeCourse,{t,0,100},PlotLegends->variables[[i]],PlotRange->Full],{i,Length[variables]}]