Year: 2026
Type: article
Abstract: We consider an autonomous system on the plane involving a parameter $\lambda $, commonly referred to as a small parameter, and with a singular point (either a center or a focus) at the origin. It is assumed that the system is isochronous at this singular point. We also assume that its isochrones – defined as the pre-images of radial lines under the transformation from the system under consideration to a system with uniform isochronicity – are independent of the parameter $\lambda $. Thus, in this paper, the parameter $\lambda $ may take on any real value and, in that sense, is not actually small. We construct systems with quadratic nonlinearities in the right-hand side that satisfy these requirements and determine their isochrones. Phase portraits of the resulting isochronous foci and their isochrones are also constructed.
Authors: A. E. Roudenok, M. N. Vasilevich
Institution: Belarusian State University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W7225586376