Alien limit cycles in Abel equations.

The aim of this paper is to study the existence of limit cycles for a family of generalized Abel equations x ′ = A (t) x m + B (t) x n , m , n ≥ 2. Under certain assumptions, it is proved that there exists a non-trivial limit cycle. This limit cycle has the characteristic that it arises from neither a Hopf bifurcation nor a perturbation of periodic orbits in a period annulus around the centre at the origin. [ABSTRACT FROM AUTHOR]