matlab - Finding the maxima of a function using ODE45

Question

I'm trying to locate the locations of one of the equations in a system of differential equations in MATLAB.I'm trying to use the Events propety of odeset.How do I pick out the particular equation in my function?

options = odeset('Events',@event);
[t x tm xm ie] = ode45(@Lorenz,[0 200],I,options);


function X = Lorenz(t,x)
r = 15;
sigma = 10;
b = 8/3;
X(1,1) = sigma*(x(2,1)-x(1,1));
X(2,1) = r*(x(1,1)) - x(2,1) -x(1,1)*x(3,1);
X(3,1) = x(1,1)*x(2,1) - b*x(3,1);
end

function [value,isterminal,direction] = event(t,x)
value  = Lorenz(t,x); %I can't specify X(3,1) here
isterminal = 0;
direction = -1;
end

In particular I'm trying to record whenever X(3,1) = 0.

Thank you

Answer 1

Basically, looking at the documentation, if you're interested in looking at when x(3) = 0, then you need to rewrite your event function:

function [value,isterminal,direction] = event(t,x)
value  = x(3); %I can't specify X(3,1) here --> why not?? Lorenz(t,x) is going to return the differential. That's not what you want
isterminal = 0;
direction = 0; %The desired directionality should be "Detect all zero crossings"
end

Now I don't know how you defined I in

[t x tm xm ie] = ode45(@Lorenz,[0 200],I,options);

But your solution to the equation is very stable around a few points and you may only see one zero crossing if x(3) at time zero is negative.

[t x tm xm ie] = ode45(@khal,[0 5],[10 -1 -20],options);
tm =

    0.1085