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

DOI10.1090/S0002-9939-00-05610-0zbMath0951.34032OpenAlexW1586982927MaRDI QIDQ4501079

Luis Angel Sanchez, Rafael Ortega

Publication date: 3 September 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-00-05610-0

zbMATH Keywords

orbital stabilitymonotone systemscompetitive systems

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Stability of solutions to ordinary differential equations (34D20) Structural stability and analogous concepts of solutions to ordinary differential equations (34D30) Monotone systems involving ordinary differential equations (34C12)

Related Items (15)

Massera's theorem for monotone dynamical systems in three dimensions ⋮ Method of ``transition into space of derivatives: 40 years of evolution ⋮ Generic behavior of flows strongly monotone with respect to high-rank cones ⋮ Periodic monotone systems having one-dimensional dynamics ⋮ Strictly monotone functions on preimages of open sets leading to Lyapunov functions ⋮ Trivial dynamics in discrete-time systems: carrying simplex and translation arcs ⋮ Generic Poincaré-Bendixson theorem for singularly perturbed monotone systems with respect to cones of rank-2 ⋮ Semiflows “Monotone with Respect to High-Rank Cones" on a Banach Space ⋮ Strictly ordered minimal subsets of a class of convex monotone skew-product semiflows. ⋮ On dynamics of generalized competitive and cooperative systems ⋮ Invariant manifolds of competitive selection-recombination dynamics ⋮ Cones of rank 2 and the Poincaré-Bendixson property for a new class of monotone systems ⋮ New generic quasi-convergence principles with applications ⋮ Convergence to equilibria in the Lorenz system via monotone methods ⋮ Unnamed Item

Cites Work

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• Homoclinic, heteroclinic, and periodic orbits for a class of indefinite Hamiltonian systems
• Orbital stability for ordinary differential equations
• Stable periodic orbits for a class of three dimensional competitive systems
• Certain differential equations have only isolated periodic orbits
• Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Existence of periodic orbits of autonomous ordinary differential equations
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets

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