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Calculus and Beyond Homework Help
Solving a System of ODE for Steady State
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[QUOTE="Bewilder, post: 5506587, member: 597786"] I am trying to find the steady states in the ODE system. Assuming y0 = 2.5 * 10^5, I want to calculate y1, y2, y3 at the steady state. I do not understand how this would be possible, because only y0 is given and the following: d0 = 0.003, d1 = 0.008, d2 = 0.05, d3 = 1, ry = 0.008, ay = 1.6/100, by = 10/750, cy = 100, u = 4 * 10^−8, y0 = 2.5 * 10^5. This is my ODE system: [ATTACH=full]188754[/ATTACH] My task says: [B]Find algebraically the steady state for the equations. Set y0 = 2.5 * 10^5 and calculate y1, y2, y3 based on the derived equations at the steady state.[/B] Is it even possible to find the exact value of y1, y2, and y3 with the given information? I have tried it in R, but it's impossible to get an answer.. How can I do this manually to get the solution for y1, y2, y3 at the steady state? [code]model <- function(t,x,params){ y0 <- x[1] y1 <- x[2] y2 <- x[3] y3 <- x[4] ry <- params[1] mu <- params[2] d0 <- params[3] ay <- params[4] d1 <- params[5] by <- params[6] d2 <- params[7] cy <- params[8] d3 <- params[9] m <- rep(0,4) m[1] = ((ry*(1-mu)) - d0) * y0 m[2] = (ay * y0) - (d1 * y1) m[3] = (by * y1) - (d2 * y2) m[4] = (cy * y2) - (d3 * y3) return(m) } x <- ode23(model, y0 = c(y0=250000, y1=y_1, y2=y_2, y3=y_3), t0=0,tf=400, params = c(0.008,4*10^-8,0.003,1.6/100,0.008,10/750,0.05,100,1))[/code] [/QUOTE]
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Solving a System of ODE for Steady State
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