Ordinary differential equations Qualitative theory Concept
Limit cycle
Summary
A limit cycle is a closed trajectory of a planar dynamical system with one property. At least one other trajectory spirals into it as time tends to or to . Limit cycles model oscillations that sustain themselves. See the definition.
Remarks
Henri Poincaré started the study of limit cycles.
Where this leads
6 pages build on this one.
Further reading
- Web https://en.wikipedia.org/wiki/Limit_cycle, lead section
About this page
| Tag | 0AAQ73WRFB |
|---|---|
| URI | m2://0AAQ73WRFB |
| Kind | concept |
| Writing | W1 stated |
| MSC | 34C07 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
- edge specializes both: the more general notions and the special cases (0 of 1)
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What links here
Definitions
Results about this
Used by
- Liénard's theorem
- Hilbert's sixteenth problem
- Homoclinic bifurcation
- Dulac's theorem on finiteness of limit cycles
- Peixoto's theorem