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Question: Numeric evolution of a system of ODEs

Question:Numeric evolution of a system of ODEs

qol90 24 Maple
August 12 2007
0
Hello, I have a problem with a system of ODEs. The three differential equations are as follows: diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000; diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)); diff(k(t),t) = 8/100*k(t) - h(t) - 1/5*k(t)*h(t); diff(c(t),t) = 2*(c(t))^2 + 21/50*c(t) - 1/100*(h(t))^2 - 1/5*c(t)*h(t) - (9/2000)*h(t) + 49/4000; diff(h(t),t) = h(t)*(c(t) - 1/5*(h(t)-1)); diff(k(t),t) = 8/100*k(t) - h(t) - 1/5*k(t)*h(t); As t goes to infinity the three variables c(t), h(t), k(t), respectively, approach certain values -in this setting 1/50, 11/10, 55/3, respectively- with the values of the derivatives converging to 0. (The point is saddle path-stable.) Now I would like to trace the evolution of the three variables for a given initial value of k(t) - say, k(0)=55/6. I have tried dsolve/numeric, but I do not know how to impose the 't to infinity' condition. Some help would be great, thanks.
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