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

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

# The critical points of this system:
CP = data.frame(x=c(-2, -1, 0, 2), y=c(0, -1, 0, 2))

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] = (2 + xt)*(yt - xt) 
    dy[2] = yt * (2 + xt - xt*2)
    list(dy)
}

diff_eq_params = list()

#postscript('../../WriteUp/Graphics/Chapter9/chap_9_sect_2_prob_10_plot.eps', onefile=FALSE, horizontal=FALSE)

t.end = 0.5
L = 2
flowField(my_yprime, x.lim = c(-L, +L), y.lim = c(-L, +L), parameters = diff_eq_params, points = 21, add = FALSE, xlab='x_1', ylab='x_2')
trajectory(my_yprime, y0 = c(1.0, 1.0), t.end = t.end, parameters = diff_eq_params, col='black', pch=19)
trajectory(my_yprime, y0 = c(1.0, -1.0), t.end = t.end, parameters = diff_eq_params, col='blue', pch=19)
trajectory(my_yprime, y0 = c(-1.0, 1.0), t.end = t.end, parameters = diff_eq_params, col='red', pch=19)
trajectory(my_yprime, y0 = c(-1.0, -1.0), t.end = t.end, parameters = diff_eq_params, col='green', pch=19)

#dev.off()