Only getting zero as my output for ode45

Hi,

So I'm producing a model based on a paper I've recently reviewed. When entering it into ode45 it only ouputs 0 as the value of X. I believe this is because X0 = 0. Though this is the correct initial condition is there anyway to work around this.

function dxdt = microalgal_model(t, X)

    uxmax = 0.275; %h-1

    %fxS variables
    kxs = 0.0624; %gSL-1  
    kixs = 12.40; %gSL-1

    %fxN variables
    kxn = 0.0812; %gNL-1
    kixn = 0.6250; %gNL-1

    %fxI variables
    kxi = 45.50; %uEm-2s-2
    kixi = 297.75; %uEm-2s-2
    o = 0.7419; %gX-1Lm-1
    l = 0.25; %m

    %fxT variables
    aox = 0.6175; %h-1
    eax = 25.9243; %Kcalmol-1
    r = 0.0099858775; %Kcalmol-1
    to = 293; %K
    box = 0.1101; %h-1
    ebx = 48.0151; %Kcalmol-1

    S = 1.05;
    N = 0.098;
    Io =125;
    T = 303;

    fxS = S / (S + kxs + ((S^2)/kixs));
    fxN = N / (N + kxn + ((N^2)/kixn));

    Il = Io*exp(-o*X*l);
    fxI = Il / (Il + kxi + ((Il^2)/kixi));

    fxT = aox * exp((-eax/r)*((1/T)-(1/to))) - box * exp ( (-ebx/r)*((1/T)-(1/to)));

    ux = uxmax * fxS * fxN * fxI * fxT;
    dxdt = ux * X;
end

tspan = [0  192];
X0 = 0;

[t, X] = ode45(@(t,X) microalgal_model(t,X), tspan, X0);

plot(t,X)

Answer 1

[Jon]

The "problem" is that x0 = 0 is an equilibrium point of your system dx/dt = 0 when x = 0.

So if you start the system at x0 = 0 then it doesn't go anywhere, it just stays at zero.

Please try for a non-zero initial condition and you will see that it infact evolves to another value.

If you don't think x0 should be an equilibrium point then you need to look further into your equations in microalgal_model as currently they evaluate to zero when x = 0

[Harry Parker]

Thanks, I had a look through the literature and found a non zero X0 value

Answer 2

[Star Strider]

Give it something other than 0 as the intial condition, for example:

X0 = 0+eps;

That worked when I tried it.