Braided connecting orbits in parabolic equations via computational homology

Research output: Contribution to JournalArticleAcademicpeer-review


We develop and present a computational method for producing forcing theorems for stationary and periodic solutions and con-necting orbits in scalar parabolic equations with periodic boundary conditions. This method is based on prior work by van den Berg, Ghrist, and Vandervorst on a Conley index theory for solutions braided through a collection of known stationary solutions. Essen-tially, the topological structure of the stationary solutions forces the existence of additional solutions with a specified topological type. In particular, this paper studies connecting orbits and devel-ops and implements the algorithms required to compute the index, providing sample results as illustrations. © 2013 Elsevier Inc.
Original languageEnglish
Pages (from-to)1086-1108
JournalJournal of Differential Equations
Publication statusPublished - 2013


Dive into the research topics of 'Braided connecting orbits in parabolic equations via computational homology'. Together they form a unique fingerprint.

Cite this