Simple non-autonomous differential equations with many limit cycles

Bartomeu Coll, Armengol Gasull, Rafel Prohens

Research output: Contribution to journalArticleResearchpeer-review

2 Citations (Scopus)


Consider the family of differential equations on the cylinder, dx/dt = a(t) + b(t) x , where x, t ∈ ℝ, and a, b are real, 1-periodic and smooth functions. The solutions satisfying x(0) = x(1) are called periodic orbits of the equation. The periodic orbits that are isolated in the set of all the periodic orbits are usually called limit cycles. We give a proof, which is self contained, that there is no upper bound for the number of limit cycles of the above type of equations.
Original languageEnglish
Pages (from-to)29-34
JournalCommunications on Applied Nonlinear Analysis
Issue number1
Publication statusPublished - 1 Jan 2008


  • Bifurcations
  • Limit cycles
  • Non-smooth differential equations


Dive into the research topics of 'Simple non-autonomous differential equations with many limit cycles'. Together they form a unique fingerprint.

Cite this