To solve boundary-value problems using shooting, click here
(R)ange | |
(2)par range | |
(L)ast | |
(O)ld | |
(G)o | |
(M)ouse | |
(S)hift | |
(N)ew | |
s(H)oot | |
(F)ile | |
form(U)la | |
m(I)ce | |
(D)AE guess | |
(B)ackward |
First choose the quantity you want to range over. It can be a parameter or a variable. The integrator will be called and this quantity will be changed at the beginning of each integration.
Then choose the starting and ending value and the number of steps.
The option Reset storage only stores the last integration. If you choose not to reset, each integration is appended to storage. Most likely, storage will be exceeded and the integration will overwrite or stop.
The option to use last initial conditions will automatically use the final result of the previous integration as initial data for the next integration. Otherwise, the current ICs will be used at each step (except of course for the variable through wich you are ranging.)
If you choose Yes in the Movie item, then after each integration, XPP will take a snapshot of the picture. You can then replay this series of snapshots back using the Kinescope.
When you are happy with the parameters, simply press the OK button. Otherwise, press the Cancel button to abort.
Assuming that you have accepted, the program will compute the trajectories and plot them storing none of them or all of them. If you press Esc it will abort the current trajectory and move on to the next.
Pressing the / key will abort the whole process.
The Crv(1) Array(2) item determines how the range is done. If you choose Crv then the two paramaters are varied in concert, [a(i),b(i)] for i=0,...,N.
The more useful Array varies them independently as [a(i),b(j)] for i=0,...,N and j=0,...,M.
The output is drawn in the current selected graphics window and the data are saved for later use.
The solution continues until either the user aborts by pressing Esc , the integration is complete, or storage runs out.
Press Enter to accept the value presented. Press Esc to quit entering and start the integration.
When a rest state has a single positive or negative eigenvalue, then XPP will ask if you want to approximate the invariant manifold. If you choose yes to this, then the initial data that were used to compute the trajectories are remembered. Thus, when you choose this option, you will be asked for a number 1-4. This number is the order in which the invariant trajectories were computed.
1 and 2 are always unstable manifolds and 3 and 4 are stable manifolds.
Note if the invariant set is a stable manifold, then you should integrate backwards in time.
When prompted for the variable, type in u[2..10] for example to set the variables u2,u3, ..., u10 and then put in a formula using the index [j] .
Note you must use [j] and not j by itself.
For example sin([j]*2*pi/10). Repeat this for different variables hitting enter twice to begin the integration.