MATLAB: Tanh gives value larger than 1

MATLABode45tanh

I'm trying to solve a set of ode with ode45. Parameter alpha_a and alpha_m are defined through a tanh function. Plotting this function gives values way larger than 1 (increasing ad infinitum), while the idea is to set a two-phase parameter that is between 0 and 1 (to estimate growth factors).
The main code is the following:
Y0 = [600; 10; 10; 0.01; 0; 0; 0];
[ts, ys] = ode45(@Pinto1, tspan, Y0); % solves the set of ode's with a general ode solver
function dBdt = Pinto1(t,B)
S = B(1); % substrate concentration
xa = B(2); % anodophilic / electrogens concentration
xm = B(3); % methanogens concentration
Mox = B(4); % oxidised mediator concentration
Q_hold = B(5); % space declaration for Q
alpha_a_hold = B(6);
alpha_m_hold= B(7);
% here are the formulas for S, xa, xm, Mox, Q
alpha_a = (1+tanh(Kx*(xa+xm-Xma)))/2; % biofilm retention fraction for electrogens
alpha_m = (1+tanh(Kx*(xa+xm-Xmm)))/2; % biofilm retention fraction for methanogens
dxadt = mua*xa - Kda*xa - alpha_a*D*xa; % electrogens concentration difference over time
dxmdt = mum*xm - Kdm*xm - alpha_m*D*xm; % methanogens concentration difference over time
% mua, Kda, mum, Kdm, and D are constants or variables defined unrelated to alpha_a and alpha_m.
dBdt = [dSdt; dxadt; dxmdt; dMoxdt; Q; alpha_a; alpha_m];
end
The calculation of S, Mox, and Q are unrelated to alpha_a and alpha_m.
My output vector contains alpha_a and alpha_m values of well over 3 within the part that I'm plotting.
As far as I know, tanh should have output values between -1 and 1.
Am I declaring my input and output wrong? Or is tanh not suited for use in an ode system? I cannot recreate the issue with just constants (leaving out xa and xm)

Best Answer

Maybe I'm getting things completely wrong, but the way I interpret your question you've plotted the last 2 components out of B returned bythe ODE-solver, and they grow in ways that "troubles" you?
If that's the case, then you've defined ODE-function such that the last two components of dBdt are alpha_a; alpha_m - meaning that the ode-solver returns the solution of the (components of the coupled ODE's) for the equations:
dF_1dt = alpha_a;
dF_2dt = alpha_m;
With alpha_a and alpha_m defined to be between 0 and 1 - this guarantees that F_1 and F_2 will grow for all times - maybe what you're interested in is the gradients of the F_1 and F_2 (last and second last component in your B) with respect to time - those would be your alpha_a and alpha_m.
HTH
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