We provide a constructive method to obtain polynomial vector fields in ℝ3 having infinitely many limit cycles starting from polynomial vector fields in ℝ2 with a period annulus. We present two examples of polynomial vector fields in ℝ3 having infinitely many limit cycles, one of them of degree 2 and the other one of degree 12. The main tools of our method are the Melnikov integral and the Hamiltonian structure. © 2013 World Scientific Publishing Company.
|Journal||International Journal of Bifurcation and Chaos|
|Publication status||Published - 1 Jan 2013|
- Limit cycle
- Melnikov integral
Ferragut, A., Llibre, J., & Pantazi, C. (2013). Polynomial vector fields in ℝ3 with infinitely many limit cycles. International Journal of Bifurcation and Chaos, 23(2), . https://doi.org/10.1142/S0218127413500296