Delay equations with rapidly oscillating stable periodic solutions

DOI10.1007/s10884-006-9068-4zbMath1204.34090OpenAlexW2039737896MaRDI QIDQ2427402

Daniel Stoffer

Publication date: 13 May 2008

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

Full work available at URL: http://doc.rero.ch/record/315221/files/10884_2006_Article_9068.pdf

zbMATH Keywords

stable periodic solutionsDelay differential equationsrapidly oscillating solutions

Mathematics Subject Classification ID

Periodic solutions to functional-differential equations (34K13) Singular perturbations of functional-differential equations (34K26)

Related Items (16)

Dependence of the dynamics of a model of coupled oscillators on the number of oscillators ⋮ Global dynamics of delay differential equations ⋮ A stable rapidly oscillating periodic solution for an equation with state-dependent delay ⋮ Exit time asymptotics for small noise stochastic delay differential equations ⋮ Saddle-node bifurcation of periodic orbits for a delay differential equation ⋮ Multiple slowly oscillating periodic solutions for $x’(t) = f(x(t-1))$ with negative feedback ⋮ Global dynamics of a differential equation with piecewise constant argument ⋮ Border-collision bifurcations from stable fixed points to any number of coexisting chaotic attractors ⋮ Relaxation modes of a system of diffusion coupled oscillators with delay ⋮ Large-amplitude periodic solutions for differential equations with delayed monotone positive feedback ⋮ Two results on stable rapidly oscillating periodic solutions of delay differential equations ⋮ Multiple periodic solutions of an equation with state-dependent delay ⋮ Dichotomy results for delay differential equations with negative Schwarzian derivative ⋮ Change of the attractor structure for \(\dot x(t) = f(x(t-1)) \) when \(f\) changes from monotone to non-monotone negative feedback ⋮ Coexistence of infinitely many large, stable, rapidly oscillating periodic solutions in time-delayed Duffing oscillators ⋮ Heteroclinic connection of periodic solutions of delay differential equations

Uses Software

• OEIS

Cites Work

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• Stable periodic solutions for delay equations with positive feedback -- a computer-assisted proof
• Heteroclinic connection of periodic solutions of delay differential equations
• Shape, smoothness and invariant stratification of an attracting set for delayed monotone positive feedback
• Stable rapidly oscillating solutions in delay differential equations with negative feedback
• Unique periodic orbits for delayed positive feedback and the global attractor

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