4 papers · 1 filter
Birkhoff center and recurrent behavior of differentially positive systems on a homogeneous space
Lin Niu, Yi Wang, Yufeng Zhang
We study the structure of the Birkhoff center and the recurrent behavior of differentially positive systems whose linearizations along trajectories preserve a homogeneous cone fiel…
Almost sure convergence of differentially positive systems on a globally orderable manifold
Lin Niu, Yi Wang, Yufeng Zhang
Differentially positive systems are nonlinear systems whose linearization along trajectories preserves a cone field on a smooth Riemannian manifold. The structures of cone field co…
Birkhoff Center and Statistical Behavior of Competitive Dynamical Systems
Xi Sheng, Yi Wang, Yufeng Zhang
We investigate the location and structure of the Birkhoff center for competitive dynamical systems, and give a comprehensive description of recurrence and statistical behavior of o…
Prevalent behavior and almost sure Poincare-Bendixson Theorem for smooth flows with invariant k-cones
Yi Wang, Jinxiang Yao, Yufeng Zhang
We investigate the global dynamics from a measure-theoretic perspective for smooth flows with invariant cones of rank k. For such systems, it is shown that prevalent (or equivalent…