On the nonchaotic nature of monotone dynamical systems

zbMath1438.37018arXiv1906.07688MaRDI QIDQ5230816

Morris W. Hirsch

Publication date: 29 August 2019

Full work available at URL: https://arxiv.org/abs/1906.07688

zbMATH Keywords

strange attractorschaotic dynamicstopological dynamicsmonotone systems

Mathematics Subject Classification ID

Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Monotone flows as dynamical systems (37C65)

Related Items (1)

Nonexistence of observable chaos and its robustness in strongly monotone dynamical systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Separable Lyapunov functions for monotone systems: constructions and limitations
• Order-preserving nonautonomous discrete dynamics: attractors and entire solutions
• Monotone dynamical systems: reflections on new advances \& applications
• Stability and convergence in discrete convex monotone dynamical systems
• Noncontinuous maps and Devaney's chaos
• Global attractivity, I/O monotone small-gain theorems, and biological delay systems
• The Poincaré-Bendixson theorem for monotone cyclic feedback systems
• Periodic competitive differential equations and the discrete dynamics of competitive maps
• Asymptotic behavior of solutions to single loop positive feedback systems
• Structural stability of Lorenz attractors
• The structure of Lorenz attractors
• On maps with dense orbits and the definition of chaos
• On the differential equations of species in competition
• A deterministic model for gonorrhea in a nonhomogeneous population
• What is topological about topological dynamics?
• Monotone dynamical systems with dense periodic points
• The puzzle of partial migration: adaptive dynamics and evolutionary game theory perspectives
• Monotone dynamical systems with polyhedral order cones and dense periodic points
• Stability and convergence in strongly monotone dynamical systems.
• The dynamical systems approach to differential equations
• Competitive and Cooperative Tridiagonal Systems of Differential Equations
• On the definition of 'chaos'
• Differential equations and convergence almost everywhere in strongly monotone semiflows
• 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
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
• On Devaney's Definition of Chaos
• The Lorenz attractor exists
• Yet Another Definition of Chaos
• Persistent properties of chaos
• Deterministic Nonperiodic Flow
• A Note on Devaney’s Definition of Chaos
• What's new on Lorenz strange attractors?

This page was built for publication: On the nonchaotic nature of monotone dynamical systems