how to stop dde23 when one of states reach certain value?

I want to stop dde23 when i am geeting 99% close to steady state and extract saturation time. I have written code of my system and then call dde23 to solve it. problem is am not able to terminate code when saturation is reached.

Answer 1

[Torsten]

Use the "Events" option of dde23.

Best wishes

Torsten.

[sourabh mittal]

function dydt = ddex1(t,y,Z)

ylag = Z(:,1);

dydt = y*ylag*(1-y)

end

sol = dde23(@ddex1,2,[0.7],[0,100]);

This is my system. when integrates with dde23, It will saturate at y =1. Now i want to get 't' when it reach 99% of its saturation value.

Please guide me how to do this using "events" function?

[Torsten]

function main
  tstart = 0.0;
  tend = 100.0;
  options = ddeset('Events',@events);
  sol = dde23(@ddex1,2,[0.7],[tstart tend],options);
  tevent = sol.xe(1)   % time of 99 % saturation
  tint = linspace(tstart,tevent,20);
  yint = deval(sol,tint);
  plot(tint,yint)
end

function dydt = ddex1(t,y,Z)
  ylag = Z(:,1);
  dydt = y*ylag*(1-y);
end

function [value,isterminal,direction] = events(t,y,Z)
  value(1) = y(1)-0.99;
  isterminal(1) = 1;
  direction(1) = 1;
end

[sourabh mittal]

Thank you!

Answer 2

[Walter Roberson]

https://www.mathworks.com/help/matlab/ref/ddeset.html

Perhaps relax RelTol ?

The normal way of stopping early is to use an event function that examines the current state and decides whether to terminate early.

However, I do not know how you would determine whether saturation has occurred. If it requires examining previous states, such as to determine that the change in values is small enough, then event functions cannot do that (but in that particular situation, changing tolerances can help.)