The Y(:,81) changes linearly with respect to T, I want to modify my code in such a way that when Y(:,81) reaches 2.5E-6 then after that it remains constant through out with T.

ti = 0;
tf = 7E-12;
tspan=[ti tf];
k = 1E-6;
h = 1E-2;
y0= [(h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1)); 
      (h)*rand(2,1); ((-3.14).*rand(1,1) + (3.14).*rand(1,1));
      ((-3.14).*rand(20,1) + (3.14).*rand(20,1));
      zeros(1,1);
      ];
yita_mn = [
    0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1;
    1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0; 
    0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 0;
    0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1;
    1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0
    ];
N = 20;
tp = 1E-12;
o = sort(10e4*rand(1,20),'ascend');
[T,Y]= ode45(@(t,y) rate_eq(t,y,yita_mn,N,o,k),tspan./tp,y0);

r = ((1/20).*( exp(i.*Y(:,3)) + exp(i.*Y(:,6)) + exp(i.*Y(:,9)) + exp(i.*Y(:,12)) + exp(i.*Y(:,15)) ...
    +exp(i.*Y(:,18)) +exp(i.*Y(:,21)) +exp(i.*Y(:,24)) + exp(i.*Y(:,27)) + exp(i.*Y(:,30)) + exp(i.*Y(:,33)) ...
    + exp(i.*Y(:,36)) + exp(i.*Y(:,39)) +exp(i.*Y(:,42)) + exp(i.*Y(:,45)) + exp(i.*Y(:,48)) + exp(i.*Y(:,51)) + exp(i.*Y(:,54))+ exp(i.*Y(:,57)) + exp(i.*Y(:,60))));



figure(1)
plot(T,Y(:,81),'linewidth',1.5)
xlabel("Time(in units of t_{p})")
ylabel("coupling")
grid on
set(gca,'fontname','times New Roman','fontsize',18,'linewidth',1.8);

%since it evolving linearly, how should I chnage the code so when it
%reaches 2E-6 it will become constant with respect to T

function dy = rate_eq(t,y,yita_mn,N,o,k)

dy = zeros(4*N+1,1);
dGdt = zeros(N,1);
dAdt = zeros(N,1);
dOdt = zeros(N,1);
P = 0.20;
a = 0;
T = 2000;
tp = 1E-12;
Gt = y(1:3:3*N-2);
At = y(2:3:3*N-1);
Ot = y(3:3:3*N-0);
for i = 1:N
    dGdt(i) = (P - Gt(i) - (1 + 2.*Gt(i)).*((At(i)))^2)./T ; 
    dAdt(i) = Gt(i)*(At(i));
    dOdt(i) = a.*Gt(i) + o(1,i).*tp;  
    for j = 1:N
        dAdt(i) = dAdt(i) + (y(81)).*yita_mn(i,j)*(At(j))*cos(Ot(j)-Ot(i));
        dOdt(i) = dOdt(i) + (y(81)).*yita_mn(i,j)*((At(j)/At(i)))*sin(Ot(j)-Ot(i));
    end
end
dy(1:3:3*N-2) = dGdt;
dy(2:3:3*N-1) = dAdt;
dy(3:3:3*N-0) = dOdt;

n1 = (1:20)';
n2 = circshift(n1,-1);
n61 = n1 +60;
n62 = circshift(n61,-1);
n80 = circshift(n61,1);

j2 =  3*(1:20)-1;
j5 = circshift(j2,-1);
j8 = circshift(j2,-2);
j59 = circshift(j2,1);

dy(n61) = (o(1,n2).' - o(1,n1).').*tp + a.*(Gt(n2) - Gt(n1)) - (y(81)).*(y(j2)./y(j5)).*sin(y(n61)) - (y(81)).*(y( j5)./y(j2)).*sin(y(n61)) + (y(81)).*(y(j8)./y(j5)).*sin(y(n62)) + (y(81)).*(y(j59)./y(j2)).*sin(y(n80));  
dy(81) = k;

end

Answer 1

[Les Beckham]

Over 100 lines of code to draw a straight line?

This plot (with the maximum Y limit applied) can be made in 8 lines of code:

T = [0 2.5 7];
Y = T*1e-6;
Y(Y>2.5e-6) = 2.5e-6; % apply the limit
plot(T,Y,'linewidth',1.5)
xlabel("Time(in units of t_{p})")
ylabel("coupling")
grid on
set(gca,'fontname','times New Roman','fontsize',18,'linewidth',1.8);