Inward linear perturbation can produce unbounded solutions

Hirokazu Ninomiya, Hans F. Weinberger

Research output: Contribution to journalArticlepeer-review


One may expect that if one adds a vector field which points toward the origin to the right-hand side of a first-order system of ordinary differential equations for which the origin is globally stable, then the origin is globally stable for the new system as well. The purpose of this note is to present an example which shows that this apparently obvious statement is, in fact, false.

Original languageEnglish (US)
Pages (from-to)1815-1818
Number of pages4
JournalMathematical Methods in the Applied Sciences
Issue number15
StatePublished - Oct 2004
Externally publishedYes


  • Blowup
  • Grow-up
  • Inward perturbation
  • Linear perturbation


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