TI-84 Plus CE field manual for IB Math
Phase portrait for a coupled system
Use sequence mode to plot one component of a coupled system against the other.
Plot a phase portrait for the coupled system x′=y, y′=−x−0.4y, x(0)=1, y(0)=0 using step size h=0.2.
Press and switch from FUNCTION to SEQ. Also switch from SEQUENTIAL to SIMUL so the coupled recurrences update from the same previous row.
Press . On the first row, move from Time to vw and press .
Press and use SEQ(n+1). Let u ( ) store time, v ( ) store x, and w ( ) store y. Enter nMin=0, u(n+1)=u(n)+0.2, u(0)=0, v(n+1)=v(n)+0.2w(n), v(0)=1, w(n+1)=w(n)+0.2(-v(n)-0.4w(n)), and w(0)=0. Type n with . In w(n+1) the leading sign inside the parentheses is a negative, not a subtraction: press (the (-) key) for it, and only for the -0.4w(n) term. The full key sequence is .
Press . Use nMin=0, nMax=40, PlotStart=1, PlotStep=1, Xmin=-1.2, Xmax=1.2, Ymin=-1.2, and Ymax=1.2.
Press .
The trajectory spirals inward toward the origin.
Your turn
Work each one on your calculator, then check the answer.
- 1
Plot the phase portrait of x′=y, y′=−2x−0.5y starting from (1.5,0) with h=0.2. Describe the behaviour.
- 2
Plot the phase portrait of x′=y, y′=x starting from (0.1,0.15) with h=0.2. Describe the behaviour.
- 3
Plot the phase portrait of x′=y, y′=−x+0.2y starting from (0.5,0) with h=0.2. Describe the behaviour.