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

# The critical points of this system:
#
CP = data.frame(
    x=c(0, 0.5),
    y=c(0, 2)
)

my_jacobian = function(x, y) {
    # returns the Jacobian at the point (x, y)
    #
    J = matrix(c(1.0 - 0.5*y, -0.5*x, 0.5*y, -0.25 + 0.5*x), 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 - 0.5*yt)
    dy[2] = yt*(-0.25 + 0.5*xt)
    list(dy)
}

diff_eq_params = list()

#postscript('../../WriteUp/Graphics/Chapter9/chap_9_sect_5_prob_2_plot.eps', onefile=FALSE, horizontal=FALSE)

t.end = 10.0
flowField(my_yprime, x.lim = c(-0.1, 2.0), y.lim = c(-0.1, 5), parameters = diff_eq_params, points = 30, add = FALSE, xlab='x', ylab='y')

# Plot some trajectories with initial condition near the critical points:
#
trajectory(my_yprime, y0 = c(0.1, 4), t.end = t.end, parameters = diff_eq_params, col='black', pch=8)
trajectory(my_yprime, y0 = c(1, 3), t.end = t.end, parameters = diff_eq_params, col='blue', pch=8)
trajectory(my_yprime, y0 = c(1, 1), t.end = t.end, parameters = diff_eq_params, col='red', pch=8)
points(CP$x, CP$y, pch=19)

#dev.off()