if( !require('phaseR') ){
    install.packages('phaseR')
}
library(phaseR)

# The critical points of this system:
#
CP = data.frame(
    x=c(0, 2, 5), 
    y=c(0, 12/5, 0)
)

my_jacobian = function(x, y) {
    # returns the Jacobian at the point (x, y)
    #
    J = matrix(c(
        1.0 - (2/5)*x - 2*y/(x+6) + 2*x*y/(x+6)^2,
        -(2*x)/(x+6),
        y/(x+6) - x*y/(x+6)^2,
        -0.25 + x/(x+6)), nrow=2, ncol=2, byrow=TRUE)
}

As = mapply(my_jacobian, CP$x, CP$y, SIMPLIFY=FALSE)
for (ii in 1:length(As)){
    es = eigen(As[[ii]])
    print(sprintf('CP: x= %f; y= %f', CP$x[ii], CP$y[ii]))
    print('Jacobian=')
    print(As[[ii]])
    print('eigenvalues=')
    print(es$values)
}

my_yprime = function(t, y, parameters) {
    xt = y[1]
    yt = y[2]
    dy = rep(NA, length(y))
    dy[1] = xt*(1.0 - 0.2 * xt - ( 2 * yt ) / (xt + 6) )
    dy[2] = yt*(-0.25 + xt / (xt + 6))
    list(dy)
}

t.end = 40.0

#postscript('../../WriteUp/Graphics/Chapter9/chap_9_sect_5_prob_13_plot.eps', onefile=FALSE, horizontal=FALSE)

diff_eq_params = list()

flowField(my_yprime, x.lim = c(-0.1, 6.0), y.lim = c(-0.1, 4.5), parameters = diff_eq_params, points = 30, add = FALSE, xlab='x', ylab='y', main=sprintf('sigma= %f', diff_eq_params$sigma))
trajectory(my_yprime, y0 = c(0.1, 4), t.end = t.end, parameters = diff_eq_params, col='black', pch=8)
points(CP$x, CP$y, pch=19)

par(mfrow=c(1, 1))

#dev.off()