Abstract:

Establishing global stability in nonlinear systems with dimension greater than two is a fundamental challenge, as the classical Bendixson–Dulac criterion is not applicable.

This talk presents a geometric approach developed by Li and Muldowney, which extends the Bendixson concept to higher-dimensional systems. The method employs the second additive compound matrix of the system’s Jacobian, together with the Lozinskii measure, to derive a rigorous stability criterion. When this measure remains uniformly negative, all two-dimensional surfaces contract, thereby ruling out periodic or other complex non-equilibrium behaviors. For systems with a unique equilibrium in a compact absorbing set, this condition guarantees global stability. The approach is illustrated using a three-dimensional SEIR epidemic model, demonstrating its effectiveness and practical value for verifying global stability through geometric analysis.

 

Organizers: Feng-Bin Wang (Chang Gung U.), Chang-Hong Wu (NYCU), Chang-Yuan Cheng (NKNU)