Lower and upper bounds for the number of limit cycles on a cylinder
- Schneider, Klaus R.
- Grin, Alexander
2010 Mathematics Subject Classification
- 34C05 34C07
- Autonomous systems with cylindrical phase space, location and number of limit cycles of second kind, Dulac--Cherkas function, factorized Dulac function
We consider autonomous systems with cylindrical phase space. Lower and upper bounds for the number of limit cycles surrounding the cylinder can be obtained by means of an appropriate Dulac-Cherkas function. We present different possibilities to improve these bounds including the case that the exact number of limit cycles can be determined. These approaches are based on the use of several Dulac-Cherkas functions or on applying some factorized Dulac function.