Singular Hopf bifurcation in a differential equation with large state-dependent delay

DOI10.1098/rspa.2013.0596zbMath1353.34086OpenAlexW2028569106WikidataQ51114068 ScholiaQ51114068MaRDI QIDQ2831313

Gregory Kozyreff, Thomas Erneux

Publication date: 2 November 2016

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2013.0596

zbMATH Keywords

Hopf bifurcationasymptotic methodsstate-dependent delay

Mathematics Subject Classification ID

Periodic solutions to functional-differential equations (34K13) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Bifurcation theory of functional-differential equations (34K18) Singular perturbations for ordinary differential equations (34E15) Asymptotic expansions of solutions to ordinary differential equations (34E05) Singular perturbations of functional-differential equations (34K26)

Related Items (7)

Periodic solutions of a singularly perturbed delay differential equation with two state-dependent delays ⋮ Generalised Lyapunov-Razumikhin techniques for scalar state-dependent delay differential equations ⋮ Resonance Phenomena in a Scalar Delay Differential Equation with Two State-Dependent Delays ⋮ Lyapunov-Razumikhin techniques for state-dependent delay differential equations ⋮ Complex oscillations in the delayed Fitzhugh-Nagumo equation ⋮ 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

• On a differential equation with state-dependent delay. A center-unstable manifold connecting an equilibrium and a periodic orbit
• Finding periodic orbits in state-dependent delay differential equations as roots of algebraic equations
• Dynamics of a delay differential equation with multiple state-dependent delays
• Criticality of Hopf bifurcation in state-dependent delay model of turning processes
• Global Hopf bifurcation for differential equations with state-dependent delay
• A two-body problem of classical electrodynamics: the one-dimensional case
• Boundary layer phenomena for differential-delay equations with state- dependent time lags. I
• Singular Hopf bifurcation in systems with fast and slow variables
• Front dynamics in a delayed-feedback system with external forcing
• Linearized stability in periodic functional differential equations with state-dependent delays
• Boundary layer phenomena for differential-delay equations with state-dependent time lags: III.
• Ikeda Hopf bifurcation revisited
• Stability of singular Hopf bifurcations
• Superstability and rigorous asymptotics in singularly perturbed state-dependent delay-differential equations
• On a model for soft landing with state-dependent delay
• Mixed-Mode Oscillations with Multiple Time Scales
• Stability and Hopf Bifurcation for a Cell Population Model with State-Dependent Delay
• Electromagnetic two-body problem: recurrent dynamics in the presence of state-dependent delay
• Singular Hopf Bifurcation in Systems with Two Slow Variables
• Nonlinear Drillstring Dynamics Analysis
• Delay induced canards in a model of high speed machining
• Singular Hopf bifurcation to strongly pulsating oscillations in lasers containing a saturable absorber
• Singular Hopf Bifurcation to Relaxation Oscillations
• On the problem of linearization for state-dependent delay differential equations
• NUMERICAL BIFURCATION ANALYSIS OF DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY
• Electromagnetic Two-Body Problem
• On the electromagnetic two-body problem

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