My first recommendation would be to use an infinite while loop. Fo starters, in pseudocode:
function StartButtonPressed
% this function executes when you hit the start button
% initialise things here
while true
k = GetValueFromSlider ; % k = current time
if k < MaxValue
k = k + 1 ; % increment time
% code to update plot here
% code to set slider value to k
end
if StopButtonPressed
break
end
end
% code to clean up things go here
