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*y, -1-2*y, -1-2*x), nrow=2, ncol=2, byrow=TRUE) } # The critical points of this system: CP = data.frame(x=c(1-sqrt(2), 0, 1+sqrt(2)), y=c(1+sqrt(2), 0, 1-sqrt(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] = yt * (2 - xt - yt) dy[2] = -xt - yt - 2*xt*yt list(dy) } diff_eq_params = list() #postscript('../../WriteUp/Graphics/Chapter9/chap_9_sect_2_prob_9_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, 1), t.end = t.end, parameters = diff_eq_params, col='black', pch=19) trajectory(my_yprime, y0 = c(1, -1), t.end = t.end, parameters = diff_eq_params, col='blue', pch=19) trajectory(my_yprime, y0 = c(-1, 1), t.end = t.end, parameters = diff_eq_params, col='red', pch=19) trajectory(my_yprime, y0 = c(-1, -1), t.end = t.end, parameters = diff_eq_params, col='green', pch=19) #dev.off()