Infinite-period bifurcation

In mathematics, an infinite-period bifurcation is a global bifurcation that can occur when two fixed points emerge on a limit cycle. As the limit of a parameter approaches a certain critical value, the speed of the oscillation slows down and the period approaches infinity. The infinite-period bifurcation occurs at this critical value. Beyond the critical value, the two fixed points emerge continuously from each other on the limit cycle to disrupt the oscillation and form two saddle points.

See also

• Heteroclinic and Homoclinic bifurcations, the two other forms of global bifurcation.
• Bifurcation theory

References

• James P. Keener, "Infinite Period Bifurcation and Global Bifurcation Branches", SIAM Journal on Applied Mathematics, Vol. 41, No. 1 (August, 1981), pp. 127–144.