Alien limit cycles in Abel equations

摘要

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. (C) 2019 Elsevier Inc. All rights reserved.