Using first integrals we introduce an alternative tool to the Poincaré maps in order to study the limit cycles of piecewise linear differential systems. It is also shown that an usual relaxation oscillation phenomenon occurrs in a two-parameter family of planar piecewise linear vector fields.
- First integrals
- Limit cycles
- Piecisewise linear differential systems
Llibre, J., Nuñez, E., & Teruel, A. E. (2002). Limit cycles for planar piecewise linear differential systems via first integrals. Qualitative Theory of Dynamical Systems, 3, 29-50. https://doi.org/10.1007/BF02969332