I want to make the K as function of time but how can I do I have no idea, the K should evolve as Y evolve.

ti = 0;
tf = 70E-8;
tspan=[ti tf];
k = 1E-3;
% I want to make this as the function of the time here, But how can I do
% this I don't have any idea, It's suppose to be like this that the as the
% Y elvolve with time same I want to do with K
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))];
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
    ]*(k);
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))));

L = (((Y(:,2) - mean(Y(:,2))).^2 + (Y(:,5) - mean(Y(:,5))).^2 + (Y(:,8) - mean(Y(:,8))).^2 + ...
    (Y(:,11) - mean(Y(:,11))).^2 +(Y(:,14) - mean(Y(:,14))).^2 +(Y(:,17) - mean(Y(:,17))).^2+ ...
    (Y(:,20) - mean(Y(:,20))).^2+(Y(:,23) - mean(Y(:,23))).^2 + (Y(:,26) - mean(Y(:,26))).^2 + ...
    (Y(:,29) - mean(Y(:,29))).^2+(Y(:,32) - mean(Y(:,32))).^2 + (Y(:,35) - mean(Y(:,35))).^2 + ...
    (Y(:,38) - mean(Y(:,38))).^2+(Y(:,41) - mean(Y(:,41))).^2 +(Y(:,44) - mean(Y(:,44))).^2 + (Y(:,47) - mean(Y(:,47))).^2+(Y(:,50) - mean(Y(:,50))).^2 +(Y(:,53) - mean(Y(:,53))).^2 + (Y(:,56) - mean(Y(:,56))).^2+(Y(:,59) - mean(Y(:,59))).^2)/19).^(0.5);

S1 = (Y(:,2) - mean(Y(:,2)))./mean(Y(:,2));
S2 = (Y(:,5) - mean(Y(:,5)))./mean(Y(:,5));
S3 = (Y(:,8) - mean(Y(:,8)))./mean(Y(:,8));
S4 = (Y(:,11) - mean(Y(:,11)))./mean(Y(:,11));
S5 = (Y(:,14) - mean(Y(:,14)))./mean(Y(:,14));
S6 = (Y(:,17) - mean(Y(:,17)))./mean(Y(:,17));
S7 = (Y(:,20) - mean(Y(:,20)))./mean(Y(:,20));
S8 = (Y(:,23) - mean(Y(:,23)))./mean(Y(:,23));
S9 = (Y(:,26) - mean(Y(:,26)))./mean(Y(:,26));
S10 = (Y(:,29) - mean(Y(:,29)))./mean(Y(:,29));
S11 = (Y(:,32) - mean(Y(:,32)))./mean(Y(:,32));
S12 = (Y(:,35) - mean(Y(:,35)))./mean(Y(:,35));
S13 = (Y(:,38) - mean(Y(:,38)))./mean(Y(:,38));
S14 = (Y(:,41) - mean(Y(:,41)))./mean(Y(:,41));
S15 = (Y(:,44) - mean(Y(:,44)))./mean(Y(:,44));
S16 = (Y(:,47) - mean(Y(:,47)))./mean(Y(:,47));
S17 = (Y(:,50) - mean(Y(:,50)))./mean(Y(:,50));
S18 = (Y(:,53) - mean(Y(:,53)))./mean(Y(:,53));
S19 = (Y(:,56) - mean(Y(:,56)))./mean(Y(:,56));
S20 = (Y(:,59) - mean(Y(:,59)))./mean(Y(:,59));

figure(1)
plot(T,abs(r),'linewidth',1.5)
xlabel("Time(in units of t_{p})")
ylabel("Order parameter")
grid on
set(gca,'fontname','times New Roman','fontsize',18,'linewidth',1.8);
ylim([0 1]);
xlim([0 8E4]);
yticks(0:0.1:1);

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

dy = zeros(4*N,1);
dGdt = zeros(N,1);
dAdt = zeros(N,1);
dOdt = zeros(N,1);
P = 0.20;
a = 1;
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) + yita_mn(i,j)*(At(j))*cos(Ot(j)-Ot(i));
        dOdt(i) = dOdt(i) + 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)) - (k).*(y(j2)./y(j5)).*sin(y(n61)) - (k).*(y( j5)./y(j2)).*sin(y(n61)) + (k).*(y(j8)./y(j5)).*sin(y(n62)) + (k).*(y(j59)./y(j2)).*sin(y(n80));  
end

[Alan Stevens]

You don't say in what way you want k to change with time.