Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2 (Q6052132)

scientific article; zbMATH DE number 7741056

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English	Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2	scientific article; zbMATH DE number 7741056

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instance of

scholarly article

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title

Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2 (English)

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Proceedings of the American Mathematical Society

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publication date

21 September 2023

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full work available at URL

https://arxiv.org/abs/2110.11783

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zbMATH Keywords

monotone systems with respect to 2-cones

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regular perturbation

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singular perturbation

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generic Poincaré-Bendixson theorem

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MaRDI profile type

MaRDI publication profile

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cites work

Geometric singular perturbation theory for ordinary differential equations

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A Perron theorem for the existence of invariant subspaces

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Semiflows “Monotone with Respect to High-Rank Cones" on a Banach Space

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Generic behavior of flows strongly monotone with respect to high-rank cones

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Boundedness of Prime Periods of Stable Cycles and Convergence to Fixed Points in Discrete Monotone Dynamical Systems

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Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets

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Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere

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Systems of differential equations which are competitive or cooperative: III. Competing species

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Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems

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Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems

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Systems of differential equations that are competitive or cooperative. VI: A local<i>C<sup>r</sup></i>Closing Lemma for 3-dimensional systems

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Non-oscillation principle for eventually competitive and cooperative systems

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Abstract competitive systems and orbital stability in $\mathbf{{\mathbb R}^3}$

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Convergence in smooth strongly monotone flows defined by semilinear parabolic equations

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Q3200297

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Convergence to cycles as a typical asymptotic behavior in smooth strongly monotone discrete-time dynamical systems

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Invariant manifolds in singular perturbation problems for ordinary differential equations

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Cones of rank 2 and the Poincaré-Bendixson property for a new class of monotone systems

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Q4834372

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Monotone dynamical systems: reflections on new advances \& applications

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Quasi Convergence and Stability for Strongly Order-Preserving Semiflows

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The Poincaré–Bendixson theorem for certain differential equations of higher order

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Existence of periodic orbits of autonomous ordinary differential equations

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Orbital stability for ordinary differential equations

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Singularly perturbed monotone systems and an Application to double phosphorylation cycles

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Dynamics alternatives and generic convergence for $C^1$-smooth strongly monotone discrete dynamical systems

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A generalization of linear positive systems with applications to nonlinear systems: invariant sets and the Poincaré-Bendixson property

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Identifiers

arXiv ID

2110.11783

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Mathematics Subject Classification ID

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Sitelinks

Mathematics(1 entry)

mardi Publication:6052132