Shilnikov's saddle-node bifurcation
By: Paul Glendinning, Colin Sparrow.
Contributors: Sparrow, Colin.; Hewlett-Packard Laboratories.
Series: [Technical report] / HP Laboratories Bristol. Basic Research Institute in the Mathematical Sciences -- HPL-BRIMS-96-07.; BRIMS technical report -- HPL-BRIMS-96-07.
Publisher: Hewlett Packard
Published: 1996
Place of publication: Bristol [England]
Language: eng
Number of pages: 10
Subjects: Bifurcation theory; Differential equations, Nonlinear; Chaotic behavior in systems
Description: Abstract: "In 1969 Shilnikov described a bifurcation for families of ordinary differential equations involving n [> or =] 2 trajectories bi-asymptotic to a non-hyperbolic stationary point. At nearby parameter values the system has trajectories in correspondence with the full shift on n symbols. We investigate a simple (piecewise smooth) example with an infinite number of homoclinic loops. We also present a smooth example which shows how Shilnikov's mechanism is related to the Lorenz bifurcation by considering the unfolding of a previously unstudied codimension two bifurcation point."
Notes: Cover title.

"To appear: International Journal of Bifurcation and Chaos: issue in honour of Leonid Shilnikov's birthday."--P. 1.

"February, 1996."

Includes bibliographical references.