Dynamic features of two ordinary differential equations with widely separated time scales

Moshe Sheintuch*, Dan Luss

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations

Abstract

A systematic approach is presented for predicting all the possible phase-plane diagrams of a system of two ordinary differential equations with widely separated time scales, and of the sequence of phase plane diagrams obtained by varying a parameter, i.e. bifurcation diagrams. The use of widely separated time scales enables the derivation of analytical algebraic expressions predicting all the transitions (bifurcations). A method is presented for a systematic finding of all the bifurcation diagrams for a system of two differential equations containing two parameters. The method is extended to systems containing many parameters. Application to the design and analysis and experimental observations are discussed.

Original languageEnglish
Pages (from-to)1653-1664
Number of pages12
JournalChemical Engineering Science
Volume40
Issue number9
DOIs
StatePublished - 1985
Externally publishedYes

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