You are absolutely awesome! It is a real pleasure to read your code and comments! I did not that it could be done in this way. Thank you!
I have not ignored your code for the autonomous system. However, in your code, you discretized the solution trajectory with respect to time, and the resulting solution points are contained in the two-dimensional (u(t),v(t)) plane; whereas I want to plot the intersection points of the solution trajectory and a specific line: u(t)=v(t), so that the expected results are discrete points on the one-dimensional line u(t)=v(t), see attached, Figure 6.5(c).
Let us back to the autonomous Duffing oscillator by setting Gamma=0, we have
With dsolve() we obtained information for [t, u(t), v(t)] and let us focused on [u(t), v(t)]. So, what I want to plot is actually the points that are both contained in the matrix [u(t),v(t)] and on the line, u(t)=v(t).
Moreover, I would like to know if there is a way to connect the discrete points in pointplot() by a smooth solid curve. I have tried the option: connect=true, and increase the sampling intervals to i=0.01, but the curve still looks furry.
Very kind wishes,