Semiflows strongly focusing monotone with respect to high-rank cones. I: Generic dynamics

2023/03/16 by Lirui Feng, Feng, Lirui
Engineering · Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2303.09691

openalex publication_date 2023/03/16 · openalex created_date 2023/03/21 · openalex updated_date 2026/07/28

Abstract

We consider a smooth semiflow strongly focusing monotone with respect to a cone of rank k on a Banach space. We obtain its generic dynamics, that is, semiorbits with initial data from an open and dense subset of any bounded open set are either pseudo-ordered or convergent to an equilibrium. For the case k=1, it is the celebrated Hirsch's Generic Convergence Theorem. For the case k=2, we obtain the generic Poincare-Bendixson Theorem.

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