Year: 2025
Type: article
Abstract: When studying traveling wave solutions of a generalized Burgers–Fisher equation we obtained a Liénard system of the form $ \frac{{\rm d}x}{{\rm d}\tau}=y, \ \frac{{\rm d}y}{{\rm d}\tau}=- x(x^{m}-1)-\varepsilon \left(a+ x^{m}\right)y $, where $ m\geq1 $ is an integer and $ \varepsilon $ is a small parameter. In this paper, we present a complete analysis for its global dynamics for all $ m\geq 1 $, giving necessary and sufficient conditions for the existence of one, two or three limit cycles and for the existence of homoclinic or double homoclinic loops by applying new methods established in this paper.
DOI: 10.11948/20250310
Authors: Maoan Han, Wenwen Hou, Wenye Liu
Institutions: Zhejiang Normal University, Heze University
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4415643868