BIFURCATION WITH MEMORY.

W Edward Olmstead*, Stephen H Davis, S. Rosenblat, William L Kath

*Corresponding author for this work

Research output: Contribution to journalArticle

41 Scopus citations

Abstract

A model equation containing a memory integral is posed. The extent of the memory, the relaxation time lambda , controls the bifurcation behavior as the control parameter R is increased. Small (large) lambda gives steady (periodic) bifurcation. There is a double eigenvalue at lambda equals lambda //1, separating purely steady ( lambda less than lambda //1) from combined steady/T-periodic ( lambda less than lambda //1) states with T yields infinity as lambda yields lambda //1** plus . Analysis leads to the co-existence of stable steady/periodic states and as R is increased, the periodic states give way to the steady states. Numerical solutions show that this behavior persists away from lambda equals lambda //1.

Original languageEnglish (US)
Pages (from-to)171-188
Number of pages18
JournalSIAM Journal on Applied Mathematics
Volume46
Issue number2
DOIs
StatePublished - Jan 1 1986

ASJC Scopus subject areas

  • Applied Mathematics

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