Passing variables to a function with lsode

[mathneuro]

I am playing around with Octave's lsode function to see if it can be a
proper MATLAB substitute for my modeling. I coded up a FH neuron and
noticed that a seemingly simple change made the code run very slowly.
I was hoping someone could help me see if the problem can be fixed.

Here is the system:

**Primary function: fhn.m**
function [y,t] = fhn
% initial condition
y0 = [0.25; 0.3];

% time vector
t = linspace(0, 100, 1000);

% ode solver
y = lsode("derivs",y,t);
end

** Secondary function: derivs.m **
function ydot = derivs(y, t)

% assignment of variables
v = y(1);
w = y(2);

% params
a = 0.25;
eps = 0.05;
gamma = 1;
I0 = 0.25;
alpha = 0;
omega = 2;

% eqns
s = alpha * sin(omega * t);
f = v * (1 - v) * (v - a);

% derivs
vdot = f - w + s + I0;
wdot = eps * (v - gamma * w);

ydot = [vdot; wdot];
end

If I make a change to pass I0 (the initial current) to the derivs
function, without using global variables, here's what I would do:

**Primary function: fhn.m**
function [y,t] = fhn(I0)
% initial condition
y0 = [0.25; 0.3];

% time vector
t = linspace(0, 100, 1000);

% ode solver
g = @(y, t) derivs(y,t,I0);
y = lsode(g,y,t,I0);
end

** Secondary function: derivs.m **
function ydot = derivs(y, t, I0)

% assignment of variables
v = y(1);
w = y(2);

% params
a = 0.25;
eps = 0.05;
gamma = 1;
% I0 = 0.25; % no longer hard coded
alpha = 0;
omega = 2;

% eqns
s = alpha * sin(omega * t);
f = v * (1 - v) * (v - a);

% derivs
vdot = f - w + s + I0;
wdot = eps * (v - gamma * w);

ydot = [vdot; wdot];
end

In my tic/toc of these two methods, the first one ran in an avg time
of about 0.14 seconds. The second one took about 3 s. I recognize that
it's passing I0 around on each iteration, and while that might not
seem meaningful in this toy example, there are plenty of uses for it.
Is there a proper way of passing I0 to derivs.m via lsode that would
make the speed difference negligible?

Thanks

[DRF]

In both versions of fh.m the second argument to lsode must be y0, not
y. As written, your programs do not run.

I don't know why you supply an extra argument to lsode in the second
version, but it does you a lot of harm. Running your program (with the
y -> y0 fix) takes 0.304 sec for the first version and 4.20 sec for
the second. When I delete the fourth argument to lsode in the second
version, it runs in 0.336 sec.

Finally, revising the first version to use a global variable for I0,
which is set from the argument of fhn, gives me a timing of 0.300 sec.