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Computing Equilibria

If you have not already done so, use the procedure of Section 1.2.12 to restore the default Lorenz System. Adjust your view window to the ${\bf {xz}}$ plane. We shall numerically compute the equilibria for the Lorenz system. First using the Panels menu button of the dstool command window, click with \framebox{MENU} on the Periodic... entry. The Periodic Orbit panel appears. (Figure [*]) The entry 0 in the Period to Find: text field in the upper left corner indicates to dstool a wish to find equilibria. Using \framebox{SELECT}, press the Find button in the fifth line of the panel, and dstool will use Newton's method starting at a random point to search for equilibria. The number of tries (by default 10) is specified in the # MC: field, and the number of equilibria found is reported in the # Found: field. Dstool marks saddles in view windows with green plus signs, sinks as blue triangles, and sources as red squares. After one or two presses of Find, you'll almost certainly have located the three saddles of the Lorenz system. (Figure [*])

To the right of Settings: on the fourth line of the Periodic Orbit panel is the Hide/Show choice box. Click \framebox{SELECT} on Show and the panel will expand, with a number of parameters accessible for editing. (Figure [*]) You can also change the Algorithm: and Initial Guess: methods via the abbreviated menu buttons to the right of these labels.


next up previous contents
Next: Computing Manifolds Up: The Lorenz Equations Previous: Loading Other Dynamical Systems   Contents
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1998-11-02