Electronic Journal of Differential Equations, Vol. 2025 (2025), No. 36, pp. 1-12.

Title: Global asymptotic stability in quadratic systems

Authors: Jaume Llibre (Univ. Autonoma de Barcelona, Catalonia, Spain)
         Claudia Valls (Univ. de Lisboa, Portugal)

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 07, 2025.
Math Subject Classifications: 34C05.
Key Words: Global asymptotic stability; planar polynomial vector fields; quadratic systems.