Prevalent behavior and almost sure Poincaré-Bendixson theorem for smooth flows with invariant $k$-cones

Attractors and repellers of smooth dynamical systems and their topological structure (37C70) Dynamics induced by flows and semiflows (37C10) Monotone flows as dynamical systems (37C65)

Cites Work

Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Unnamed Item
Monotone dynamical systems: reflections on new advances \& applications
On the equivalent classification of three-dimensional competitive Leslie/Gower models via the boundary dynamics on the carrying simplex
Generic behavior of flows strongly monotone with respect to high-rank cones
The Poincaré-Bendixson theorem for monotone cyclic feedback systems
Smoothness of the carrying simplex for discrete-time competitive dynamical systems: A characterization of neat embedding
Existence of periodic orbits for high-dimensional autonomous systems
Orbital stability for ordinary differential equations
Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems
A Perron theorem for the existence of invariant subspaces
The $C^ 1$ property of carrying simplices for a class of competitive systems of ODEs
Convergence in smooth strongly monotone flows defined by semilinear parabolic equations
The Poincaré-Bendixson theorem for monotone cyclic feedback systems with delay
Carrying simplices for competitive maps
$k$-contraction: theory and applications
Dynamics alternatives and generic convergence for $C^1$-smooth strongly monotone discrete dynamical systems
Linearization and invariant manifolds on the carrying simplex for competitive maps
$K$-dimensional invariant cones of random dynamical systems in $\mathbb{R}^n$ with applications
Prevalent behavior of strongly order preserving semiflows
Tensor products, positive linear operators, and delay-differential equations
On sets of Haar measure zero in abelian Polish groups
A generalization of linear positive systems with applications to nonlinear systems: invariant sets and the Poincaré-Bendixson property
Semiflows “Monotone with Respect to High-Rank Cones" on a Banach Space
Stability and convergence in strongly monotone dynamical systems.
Jacobi matrices and transversality
The dynamical systems approach to differential equations
Prevalent behavior of smooth strongly monotone discrete-time dynamical systems
Lyapunov exponents and invariant manifolds for random dynamical systems in a Banach space
Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
Systems of differential equations which are competitive or cooperative: III. Competing species
Existence of periodic orbits of autonomous ordinary differential equations
Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
Convergence for Strongly Order-Preserving Semiflows
Prevalence: a translation-invariant “almost every” on infinite-dimensional spaces
Abstract competitive systems and orbital stability in $\mathbf{{\mathbb R}^3}$
Geometry of carrying simplices of 3-species competitive Lotka–Volterra systems
The property of convex carrying simplices for competitive maps
Haar null and Haar meager sets: a survey and new results
Monotone control systems
Discrete-Time $k$-Positive Linear Systems
The general properties of dicrete-time competitive dynamical systems

This page was built for publication: Prevalent behavior and almost sure Poincaré-Bendixson theorem for smooth flows with invariant $k$-cones

Prevalent behavior and almost sure Poincaré-Bendixson theorem for smooth flows with invariant \(k\)-cones