# proj matrix A
A <- rbind(c(0,0,0,0,127,4,80),
           c(.6747,.737,0,0,0,0,0),
           c(0,.0486,.661,0,0,0,0),
           c(0,0,.0147,.6907,0,0,0),
           c(0,0,0,.0518,0,0,0),
           c(0,0,0,0,.8091,0,0),
           c(0,0,0,0,0,.8091,.8089))

V <- eigen(A)
D <- V$vectors
V <- V$values

n_zero <- c(2900,
            9000,
            1600,
            100,
            5,
            4,
            20)
    
                
Tmax <- 200
n_vs_t <- matrix(0, 7, Tmax)
n_vs_t[,1] <- n_zero

for (t in 2:Tmax)
  n_vs_t[,t] <- A %*% n_vs_t[,t-1]

matplot(1:Tmax, t(n_vs_t), type = "l",
        xlab = "t", ylab = "n")
legend("topright", paste("stage =",1:7), col = 1:7, lty = 1:7)