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How to define event function in ode45 solver as the slop of variable achieve certain value?

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H_W
H_W 2022-5-4
评论： H_W 2022-5-4
Hi! I want to solve the Van Der Pol equations using ode45 with event function as its stopping criteria. I would like to set the stopping criteria as the slope of is small enough:
where is the change of the value of at the nearest time step and its previous time step.
I am not sure can event function access the value of both at the current time and the previous time, since it seems that the events function receives both the current time and the current state vector.
In this case, how to revise the code? Thanks a lot for any suggestion!
Here is the code
function main
options = odeset('Events',@event_function);
initial_cond = [2;0;0];
[t,y] = ode45(@vanderpol,[0 20],initial_cond,options);
plot(t,y(:,1),'-o',t,y(:,2),'-o',t,y(:,3),'-o');
title('Solution of van der Pol Equation (\mu = 1) with ODE45');
xlabel('Time t');
ylabel('Solution y');
legend('y_1','y_2','z');
function dydt = vanderpol(t,y)
dydt = [y(2); (1-y(1)^2)*y(2)-y(1); y(1)^2+y(2)^2];
function [value,isterminal,direction] = event_function(t,y)
value = y(1)-0.1; % when value = 0, an event is triggered
isterminal = 1; % terminate after the first event
direction = 0; % get all the zeros

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Torsten
Torsten 2022-5-4
编辑：Torsten 2022-5-4
Maybe someone could answer if he/she knew what z is in your code. Is it y(1), y(2) or y(3) ?
Anyhow: The slopes of your variables is given by
dydt = [y(2); (1-y(1)^2)*y(2)-y(1); y(1)^2+y(2)^2];
So choose the one you need to specify your event.
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