Problem with input of ode113

I'm trying to run a very simple ODE. However when running it Matlab shows me the error: 'Index in position 1 exceeds array bounds (must not exceed 1)' for I_2 in the QIF function.

My code is posted below:

I_1=  pi^2;
I_2= -2*pi^2;

params.tau= 10;
g= 0;

V_1= -65;
V_2= -65;

state= [V_1;V_2];
I= [I_1;I_2];

options = odeset('abstol',1e-8,'reltol',1e-8);

[t,state] = ode113(@QIF,[1 3000],state,I,params)

With QIF :

function [statep]= QIF(t,state,I,params);
I_1= I(1);
I_2=I(2);

v= (state(1)+state(2))/length(state);

V_1d= ((state(1)^2)+ I_1)/params.tau;
V_2d= ((state(2)^2)+ I_2)/params.tau;

statep= [V_1d,V_2d]

Does anyone see what I don't see?

Answer 1

[Stephan]

I_1=  pi^2;
I_2= -2*pi^2;
params.tau= 10;
g= 0;
V_1= -65;
V_2= -65;
state= [V_1;V_2];
I= [I_1;I_2];
options = odeset('abstol',1e-8,'reltol',1e-8);
[t,state] = ode113(@(t,state)QIF(t,state,I,params),[1 10.8],state,options);
plot(t,state)

function statep= QIF(~,state,I,params)
I_1= I(1);
I_2=I(2);
V_1d= ((state(1)^2)+ I_1)/params.tau;
V_2d= ((state(2)^2)+ I_2)/params.tau;
statep = [V_1d;V_2d];
end

For t>10.84627 your function gives a warning due to the extreme rise of the resulting values. Maybe you should check if your implementation is correct.

[Maarten Duijn]

Thanks Stephan for the quick response.

Yes it is indeed correct that my state (which represent membrane potential) goes to infinity at a certain point. I plan on implementing a discrete resetting rule when this happens. Do you have a hint how to implement that in the ode solver?

[Stephan]

Sounds like you might want to use ode events to tackle this. In the given link there is an example of a jumping ball - i suspect this is the kind of thing you want to do.

[Maarten Duijn]

Yes, thats kind of what I want to use. I used the event function of the ballode function and the event outputs. However, the event function does not recognize the value at which it needs to terminate the ode solver.

function [value,isterminal,direction] = QIF_reset(t,y)
% Locate the time when height passes through zero in a decreasing direction
% and stop integration.
value =100-y(1);     % detect height = 0
isterminal = 1;   % stop the integration
direction = -1;   % negative direction

The ode will keep solving past the event of y(1) reaching 100.