CHEN 3201 Lecture Notes - Lecture 37: Saddle Point, Limit Cycle, Periodic Point
12 Apr 2015
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If it"s stable, all the eigenvalues are negative. Numerically, we will never stay @ unsteady state b/c even the smallest error associated w/ any numerical methods (round-off errors) Even as accurate as we try to get, we will still have enough error to fall out of unsteady state. Phase planes & dynamic systems y1 and y2 can be anything like t and p, conc. and t, Chen3201_numericalmethods page 2 we have steady states and the plot shows how y1 and y2 get to their steady states. Phase plane steady state initial condition (look @ what the initial values were for y1 and y2. In this problem, time is implicit (it"s the independent variable, but we only care about how y1 and y2 move relative to each other, not how fast they move) Compute the eigenvalues of the jacobian @ the steady state.
