Structure of the global attractor of cyclic feedback systems

DOI10.1007/BF02218817zbMath0823.34057OpenAlexW2008608018MaRDI QIDQ1347233

Tomáš Gedeon, Konstantin Mischaikow

Publication date: 4 April 1995

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02218817

zbMATH Keywords

Lyapunov functionglobal compact attractorMorse decompositioncyclic feedback systemsMorse setsMorse-Smale dynamicsset of connecting orbits

Mathematics Subject Classification ID

Attractors of solutions to ordinary differential equations (34D45) Morse-Smale systems (37D15)

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Cites Work

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• Stable periodic solutions for the hypercycle system
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• The Poincaré-Bendixson theorem for monotone cyclic feedback systems
• Integral averaging and bifurcation
• Zeta functions, periodic trajectories, and the Conley index
• A refinement of the Conley index and an application to the stability of hyperbolic invariant sets
• Global Asymptotic Dynamics of Gradient-Like Bistable Equations
• On the global dynamics of attractors for scalar delay equations

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