Front dynamics in a delayed-feedback system with external forcing

DOI10.1016/S0167-2789(03)00175-1zbMath1085.34057MaRDI QIDQ1404835

Michel Nizette

Publication date: 24 August 2003

Published in: Physica D (Search for Journal in Brave)

zbMATH Keywords

stabilitycontinuous periodic-solution deformationscalar nonlinear delay-differential equation

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Transformation and reduction of functional-differential equations and systems, normal forms (34K17) Lasers, masers, optical bistability, nonlinear optics (78A60) Singular perturbations of functional-differential equations (34K26) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (11)

Ikeda Hopf bifurcation revisited ⋮ Normal and quasinormal forms for systems of difference and differential-difference equations ⋮ Spatio-temporal phenomena in complex systems with time delays ⋮ Metastable periodic patterns in singularly perturbed state-dependent delayed equations ⋮ Bifurcation analysis of a normal form for excitable media: Are stable dynamical alternans on a ring possible? ⋮ Metastable periodic patterns in singularly perturbed delayed equations ⋮ Exponential asymptotics of localised patterns and snaking bifurcation diagrams ⋮ Singular Hopf bifurcation in a differential equation with large state-dependent delay ⋮ Delay-induced switched states in a slow–fast system ⋮ Stability and Hopf bifurcations of an optoelectronic time-delay feedback system ⋮ Hopf bifurcations in time-delay systems with band-limited feedback

Cites Work

• Unnamed Item
• High-dimensional chaotic behavior in systems with time-delayed feedback
• Long time behavior of solutions of bistable nonlinear diffusion equations
• The approach of solutions of nonlinear diffusion equations to travelling front solutions
• Collision and collapse of layers in a 1D scalar reaction-diffusion equation
• Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
• Multiple scale analysis of delayed dynamical systems
• Front Propagation in Heterogeneous Media

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