Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations

DOI10.1016/j.jde.2010.10.024zbMath1227.34072OpenAlexW2057598198MaRDI QIDQ2430950

John Mallet-Paret, Roger D. Nussbaum

Publication date: 8 April 2011

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

Full work available at URL: https://doi.org/10.1016/j.jde.2010.10.024

zbMATH Keywords

stabilitysingular perturbationperiodic solutionstate-dependent delaydelay-differential equationslimit profile

Mathematics Subject Classification ID

Asymptotic theory of functional-differential equations (34K25) Stability theory of functional-differential equations (34K20) Periodic solutions to functional-differential equations (34K13) Singular perturbations of functional-differential equations (34K26)

Related Items (26)

Existence, Uniqueness, and Stability of Slowly Oscillating Periodic Solutions for Delay Differential Equations with Nonnegativity Constraints ⋮ A differential equation with state-dependent delay from cell population biology ⋮ An analysis on the stability of a state dependent delay differential equation ⋮ John Mallet-Paret 60 ⋮ Periodic solutions of a singularly perturbed delay differential equation with two state-dependent delays ⋮ Exit time asymptotics for small noise stochastic delay differential equations ⋮ Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations ⋮ Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays ⋮ Stability of nonlinear differential systems with state-dependent delayed impulses ⋮ The existence of periodic solutions for second-order delay differential systems ⋮ Floquet multipliers of a periodic solution under state-dependent delay ⋮ Analytic solutions of delay-differential equations ⋮ Stability of periodic solutions of state-dependent delay-differential equations ⋮ Traveling wave solutions of a reaction-diffusion equation with state-dependent delay ⋮ A condition on delay for differential equations with discrete state-dependent delay ⋮ Metastable periodic patterns in singularly perturbed state-dependent delayed equations ⋮ Periodic solutions of delay differential systems via Hamiltonian systems ⋮ Dynamics of a Mathematical Hematopoietic Stem-Cell Population Model ⋮ Numerical approaches for state-dependent neutral delay equations with discontinuities ⋮ Lyapunov-Razumikhin techniques for state-dependent delay differential equations ⋮ Solution manifolds which are almost graphs ⋮ Singular Hopf bifurcation in a differential equation with large state-dependent delay ⋮ Solutions of mixed-type functional differential equations with state-dependence ⋮ Intricate structure of the analyticity set for solutions of a class of integral equations ⋮ Nonlinear effects of instantaneous and delayed state dependence in a delayed feedback loop ⋮ Bifurcation analysis of systems with delays: methods and their use in applications

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Linearized stability for semiflows generated by a class of neutral equations, with applications to state-dependent delays
• Linearizing equations with state-dependent delays
• Dynamic hematological disease: a review
• Center-stable manifolds for differential equations with state-dependent delays
• Algebraic-delay differential systems, state-dependent delay, and temporal order of reactions
• Commodity price fluctuations: Price dependent delays and nonlinearities as explanatory factors
• Insight into the transfer function, gain, and oscillation onset for the pupil light reflex using nonlinear delay-differential equations
• Modelling autonomous oscillations in the human pupil light reflex using nonlinear delay-differential equations
• A two-body problem of classical electrodynamics: the one-dimensional case
• Geometric singular perturbation theory for ordinary differential equations
• Boundary layer phenomena for differential-delay equations with state- dependent time lags. I
• Periodic solutions of some nonlinear autonomous functional differential equations
• Some periodicity criteria for functional differential equations
• Existence of periodic solutions for delay differential equations with state dependent delay
• Introduction to functional differential equations
• Periodic solutions for functional differential equations with multiple state-dependent time lags
• On differentiability of solutions with respect to parameters in state-dependent delay equations
• A local unstable manifold for differential equations with state-dependent delay
• The solution manifold and \(C^{1}\)-smoothness for differential equations with state-dependent delay.
• Stable periodic motion of a system using echo for position control
• Existence of periodic solutions for a state dependent delay differential equation
• Semigroup properties and the Crandall Liggett approximation for a class of differential equations with state-dependent delays
• Consumer memory and price fluctuations in community markets: An integrodifferential model
• Uniqueness of solutions of state dependent delay differential equations
• Stable periodic motion of a system with state dependent delay.
• Periodic solutions for differential equations with state-dependent delay and positive feedback
• Boundary layer phenomena for differential-delay equations with state-dependent time lags: III.
• Delay equations. Functional-, complex-, and nonlinear analysis
• Asymptotic theory for a class of functional differential equations with state-dependent delays
• A periodic solution of a differential equation with state-dependent delay
• Erratum to ``On a model of a currency exchange rate-local stability and periodic solutions [J. Dynam. Diff. Eq. 16, 393-432 (2004)]
• Stability of periodic solutions of state-dependent delay-differential equations
• On a model for soft landing with state-dependent delay
• Exponential stability of a state-dependent delay system
• Asymptotic theory for the delay-differential equation \(u'(t) =-au(t- r(u(t)))\)
• Uniqueness of the zero solution for delay differential equations with state dependence
• Analysis of a Model Representing Stage-Structured Population Growth with State-Dependent Time Delay
• Slowly oscillating periodic solutions of autonomous state-dependent delay equations
• On the problem of linearization for state-dependent delay differential equations
• Boundary layer phenomena for differential-delay equations with state dependent time lags: II.
• The fixed point index and asymptotic fixed point theorems for $k$-set-contractions
• The two-dimensional attractor of a differential equation with state-dependent delay

This page was built for publication: Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations