Jaume Llibre, Claudia Valls
Abstract:
A classical problem in the qualitative theory of differential systems that
is relevant for its applications, is to characterize the differential
systems which are globally asymptotically stable, that is differential
systems having a unique equilibrium point for which all their orbits,
with the exception of the equilibrium point, tend in forward time to this
equilibrium point.
Here we provide three conditions that characterize the global asymptotic
stability for planar quadratic polynomial differential systems.
Using these three conditions we characterize all planar quadratic polynomial
differential systems that are globally asymptotically stable.
Submitted June 2, 2024. Published April 7, 2025.
Math Subject Classifications: 34C05.
Key Words: Global asymptotic stability; planar polynomial vector fields; quadratic systems.
DOI: 10.58997/ejde.2025.36
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Jaume Llibre Departament de Matemàtiques Universitat Autònoma de Barcelona 8193 Bellaterra, Barcelona, Catalonia, Spain email: jaume.llibre@uab.cat |
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| Claudia Valls Departamento de Matemática Instituto Superior Técnico, Universidade de Lisboa Av. Rovisco Pais 1049-001, Lisboa, Portugal email: claudia.valls@tecnico.pt |
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