close allsyms W(t);W(t) = piecewise(3/12<=t<=8/12, 1,t>=1, W(t-1) ,0);t(1) = 0;y1(1) = 600;y2(1) = 1000;h = 0.5;t_end = 5;t = 0:h:t_end;a = 2;c = 3;alfa = 10^-3;gamma = 6*10^-3;f = @(t,y1,y2) (a-alfa*y2)*y1-W(t)*y1;g = @(t,y1,y2) (-c+gamma*y1)*y2;for i = 1:(length(t)-1) k1 = f(t(i),y1(i),y2(i)); l1 = g(t(i),y1(i),y2(i)); k2 = f(t(i)+h/2,(y1(i)+0.5*k1*h),(y2(i)+(0.5*l1*h))); l2 = g(t(i)+h/2,(y1(i)+0.5*k1*h),(y2(i)+(0.5*l1*h))); k3 = f(t(i)+h/2,(y1(i)+0.5*k2*h),(y2(i)+(0.5*l2*h))); l3 = g(t(i)+h/2,(y1(i)+0.5*k2*h),(y2(i)+(0.5*l2*h))); k4 = f(t(i)+h,(y1(i)+k3*h),(y2(i)+l3*h)); l4 = g(t(i)+h,(y1(i)+k3*h),(y2(i)+l3*h)); y1(i+1) = y1(i) + (k1 +2*k2 +2*k3 +k4)*(h/6); y2(i+1) = y2(i) + (l1 +2*l2 +2*l3 +l4)*(h/6); ystar=[y1', y2']; end
This code is for the implementation of a predator-prey model/ volterra-lotka model using the time integration method RK4. There is a t dependent (W(t)) variable in the function. How can these bounded values be implemented on matlab? Especially the W(t-1) part, this part will look at the previous boundaries.
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