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Question: Plotting SADDLE PATH

Question:Plotting SADDLE PATH

Peter Panakx 4 Maple
coordinates plot
May 07 2010
0
How can I plot saddle path (trajectory) in dynamic system of two differential equations? I am trying to plot saddle path of Ramsey-Cass-Koopmans growth model in Maple 13, but I can't get the trajectory that goes to steady state. The system is following: > alpha := .5; theta := 1; rho := 0.5e-1; n := 0.1e-1; g := 0.2e-1; delta := 0.3e-1; > nulc := plot([((delta+rho+theta*g)/alpha)^(1/(alpha-1)), c, c = 0 .. 10], color = black, thickness = 2, labels = ["k", "c"]); nulk := plot(k(t)^alpha-(n+g+delta)*k(t), k = 0 .. 100, color = black, thickness = 2, labels = ["k", "c"]); > RAMSEY := {diff(c(t), t) = c(t)*(alpha*k(t)^(alpha-1)-delta-rho-theta*g)/theta, diff(k(t), t) = k(t)^alpha-c(t)-(n+g+delta)*k(t)}; > kss := ((delta+rho+theta*g)/alpha)^(1/(alpha-1)); css := ((delta+rho+theta*g)/alpha)^(alpha/(alpha-1))-(n+g+delta)*((delta+rho+theta*g)/alpha)^(1/(alpha-1)); > ivp := {[k(0) = kss, c(0) = css]}; > with(plots); with(DEtools); > phase := DEplot(RAMSEY, [k(t), c(t)], t = -10 .. 10, ivp, k = 0 .. 100, c = 0 .. 10, arrows = small, title = `Ramseyho model`, color = magnitude); > display({nulc, nulk, phase}); where alpha..delta are parameters, nulc is nulcline for c, nulk is nulcline for k, RAMSEY is the system, kss and css are steady state values of c and k (coordinates of saddle point)... I just need to get that saddle path... Anyone can help me?
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