Alien limit cycles in Abel equations
The authors consider the generalized Abel equation \[ \frac{dx}{dt}=\left(a_{1}A_{1}(t)+a_{2}A_{2}(t)\right)x^m+\left(a_{3}A_{3}(t)+a_{4}A_{4}(t)\right)x^n, \] where \(t, {a}_{i}\in \mathbb{R}\), \(i=\overline{1,4}\); \(m, n\in \mathbb{N}\), \(m>n\ge 2\). Sufficient conditions are obtained under which the generalized Abel equation has a so-called alien limit cycle, i.e., limit cycle that arises from neither a Hopf bifurcation nor a perturbation of periodic orbits in a period annulus around the centre at the origin.
scientific article; zbMATH DE number 7138382
scientific article