Hi all,
hopefully the Sourceforce community is doing well and is safe.
The init_H_LC function in Matcont seems convenient for calculating an initial Limit Cycle at a Hopf bifurcation. Nevertheless, I wonder:
1) At the Hopf bifurcation of a smooth differential equation, limit cycles are born starting at zero amplitude, or am I wrong? Then how do we achieve a finite amplitude there, is it due to the fact, that numerical precision leads to the root of the test function being found slightly offset of the real bifurcation?
2) How is it explained that by varying the tolerance option, we are having limit cycles of different size? Shouldn't each parameter value correspond to one (or perhaps a few periodic solutions, if the branches change direction)?
3) Does this function work with the "shooting" method, or with the Poincare method for finding period solutions?
Best regards
lanast
Last edit: lanast 2020-03-30
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Hi all,
hopefully the Sourceforce community is doing well and is safe.
The init_H_LC function in Matcont seems convenient for calculating an initial Limit Cycle at a Hopf bifurcation. Nevertheless, I wonder:
1) At the Hopf bifurcation of a smooth differential equation, limit cycles are born starting at zero amplitude, or am I wrong? Then how do we achieve a finite amplitude there, is it due to the fact, that numerical precision leads to the root of the test function being found slightly offset of the real bifurcation?
2) How is it explained that by varying the tolerance option, we are having limit cycles of different size? Shouldn't each parameter value correspond to one (or perhaps a few periodic solutions, if the branches change direction)?
3) Does this function work with the "shooting" method, or with the Poincare method for finding period solutions?
Best regards
lanast
Last edit: lanast 2020-03-30