Determining the steady-state concentrations using your numerical solutions.

What are the dynamics? How do you determine the steady-state concentrations using numerical solutions?

Plot should look like the following

File 1

function dYdt = lab1_model(t,Y)  % TODO - Write the function declaration. 
    % Name of the function is lab1_model

    % TODO - Extract a, b, c, and d from input vector Y
    a = Y(1); 
    b = Y(2);
    c = Y(3); 
    d = Y(4);
    
    % TODO - Define the constants k1 through k5
    k1 = 3; % mM/s
    k2 = 2; % 1/s
    k3 = 2.5; % 1/mM*s
    k4 = 3; % 1/s 
    k5 = 4; % 1/s
    
    % TODO - Define dadt, dbdt, dcdt, dddt from the ODEs
    dadt = k1 - k2 * a - k3 * a * b;
    dbdt = k2 * a - k3 * a * b;
    dcdt = k3 * a * b - k4 * c;
    dddt = k3 * a * b - k5 * d;

    % Create output column vector dYdt
    dYdt = [dadt; dbdt; dcdt; dddt];

end 

File 2

clear all

% TODO define the timespan to simulation
tRange = [0 4];

% TODO define the initial conditions
Y0 = [0; 0; 0; 0;];

% call the solver of choice (ode45 is fine)
[tSol,YSol] = ode15s(@(tSol,YSol)lab1_model(tSol,YSol),tRange,Y0);

% plot solutions to look like figure in lab
A = plot(tSol,YSol(:,1),'b','LineWidth',2);
hold on
B = plot(tSol,YSol(:,2),'m','LineWidth',2);
C = plot(tSol,YSol(:,3),'g','LineWidth',2);
D = plot(tSol,YSol(:,4),'r','LineWidth',2);

% make axis labels and change linestyles as desired
xlabel('Time (sec)')
ylabel('Concentration (mM)')
A.LineStyle = '-';
B.LineStyle = '--';
C.LineStyle = ':';
D.LineStyle = '-.';

% make a legend
legend({'A', 'B', 'C', 'D'}, 'Location','southeast')

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Torsten]

Set dadt,dbdt,dcdt and dddt to 0 and solve the algebraic system in a,b,c,d using fsolve, e.g.