Limit orbit above Hopf bifurcation, derived by time integration
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Hello together,
in order to "continue" branches of limit cycles above the Hopf bifurcation point, I am simulating the system's response with ode15s by giving the system a slight disturbance at a parameter just above the Hopf point. Indeed, a stable (for the supercritical case) limit cycle appears, which I am feeding into initOrbLC. Are there general guidelines for the extent of time history, that this function requires, besides being between 1x and 2x of the period? I am realizing that the amount of points influences the system performance later, during continuation..
Thanks, and a nice weekend
lanast
Last edit: lanast 2020-02-01
Dear Ianast,
For InitOrbLC, that's indeed the strategy.
You pick up the final point and then do a simulation for something like 1.1-1.5 times the period.
The number of mesh points (40 is a good choice normally) only needs to be high if the shape of your periodic orbit requires that.
Best, Hil
From: lanast lanast@users.sourceforge.net
Sent: Saturday, February 1, 2020 5:03 PM
To: [matcont:discussion]
Subject: [matcont:discussion] Limit orbit above Hopf bifurcation, derived by time integration
Hello together,
in order to "continue" branches of limit cycles above the Hopf bifurcation point, I am simulating the systems response with ode15s by giving the system a slight disturbance at a parameter just above the Hopf point. Indeed, a stable (for the supercritical case) limit cycle appears , which I am feeding into initOrbLC. Are there general guidelines for the extent of time history, that this function requires, besides being between 1x and 2x of the period? I am realizing that the amount of points influences the system performance later, during continuation..
Thanks, and a nice weekend
lanast
Limit orbit above Hopf bifurcation, derived by time integration
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Thank you for this hint Hil