Difference between limit point cycle and limit point 'of' cycle.

[vr98]

When we continue the system we have from a Hopf bifurcation point detected by matcont, we get MaxNumPoints number of limit cycles and one limit point cycle. I went through the manuals, but my confusion persists. Is limit point cycle different from limit point 'of' cycle?

I understand that limit point of cycle is a fold bifurcation on a limit cycle. But the matcont message shows 'limit point cycle'. What exactly does that indicate?

[hilmeijer]

There is no difference, but in our code/message we just dropped the "of".

The message means LPC=Limit Point (of) Cycles=Saddle-node of cycles

(but it is NOT a saddle-node of equilibria on the cycle)

Best regards, Hil

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From: vr98 vr98@users.sourceforge.net
Sent: Tuesday, July 23, 2019 7:08 AM
To: [matcont:discussion]
Subject: [matcont:discussion] Difference between limit point cycle and limit point 'of' cycle.

WhenI continue the system we have from a Hopf bifurcation point detected by matcont, we get MaxNumPoints number of limit cycles and one limit point cycle. I went through the manuals, but my confusion persists. Is limit point cycle different from limit point of cycle?

I understand that limit point of cycle is a fold bifurcation on a limit cycle. But the matcont message shows 'limit point cycle'. What exactly does that indicate?

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Difference between limit point cycle and limit point 'of' cycle.

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