Flip Bifurcation in Dynamical Systems

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

A flip bifurcation occurs when increasing the parameter causes the graph of the function or to intersect the line . See Example 2.32 of [1]. In a flip bifurcation, an eigenvalue leaves the unit circle through the point . When this happens, the period two points become stable; thus, this is also known as a period-doubling bifurcation. Varying , the zero solution becomes unstable for ; the period one blue branch becomes unstable for ; the period-doubling bifurcation occurs at . At the period-doubling bifurcation, the fixed points of become stable.

Contributed by: Edmon Perkins (October 2018)
After work by: Ali Nayfeh and Balakumar Balachandran
Open content licensed under CC BY-NC-SA


Details

Reference

[1] A. H. Nayfeh and B. Balachandran, Applied Nonlinear Dynamics: Analytical, Computational, and Experimental Methods, New York: Wiley, 1995.


Snapshots



Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.
Send