Local Theory for Spatio-Temporal Canards and Delayed Bifurcations
From MaRDI portal
Publication:5137076
DOI10.1137/19M1306610zbMath1453.35020arXiv1912.06205MaRDI QIDQ5137076
Martin Wechselberger, Daniele Avitabile, Romain Veltz, Mathieu Desroches
Publication date: 1 December 2020
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1912.06205
Reaction-diffusion equations (35K57) Partial functional-differential equations (35R10) Bifurcations in context of PDEs (35B32) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)
Related Items (1)
Uses Software
Cites Work
- Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations
- Stability of traveling pulses with oscillatory tails in the FitzHugh-Nagumo system
- Multiple time scale dynamics
- Invariant manifolds for flows in Banach spaces
- Local bifurcations, center manifolds, and normal forms in infinite-dimensional dynamical systems
- Chasse au canard
- Canard solutions and travelling waves in the spruce budworm population model
- Dynamic transcritical bifurcations in a class of slow-fast predator-prey models
- Canards and bifurcation delays of spatially homogeneous and inhomogeneous types in reaction-diffusion equations
- Center manifolds and contractions on a scale of Banach spaces
- Geometric singular perturbation theory for ordinary differential equations
- Singularities and groups in bifurcation theory. Volume II
- Introduction to functional differential equations
- A Hartman-Grobman theorem for the Cahn-Hilliard and phase-field equations
- On delayed oscillation in nonspatially uniform FitzHugh Nagumo equation
- Invariant manifolds for parabolic partial differential equations on unbounded domains
- Invariant manifolds of partial functional differential equations.
- Travelling waves in a chain of coupled nonlinear oscillators
- Slow passage through a Hopf bifurcation in excitable nerve cables: spatial delays and spatial memory effects
- On the Lambert \(w\) function
- Relaxation oscillations in \({\mathbb R}^3\)
- Delay equations. Functional-, complex-, and nonlinear analysis
- Fourier series, Fourier transform and their applications to mathematical physics
- Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems
- Fold points and singularity induced bifurcation in inviscid transonic flow
- Extending Geometric Singular Perturbation Theory to Nonhyperbolic Points---Fold and Canard Points in Two Dimensions
- Infinite Dimensional Geometric Singular Perturbation Theory for the Maxwell--Bloch Equations
- Extending slow manifolds near transcritical and pitchfork singularities
- A Center Manifold Result for Delayed Neural Fields Equations
- Existence of Traveling Wave Solutions for a Model of Tumor Invasion
- À propos de canards (Apropos canards)
- Mixed-Mode Oscillations with Multiple Time Scales
- Excitability in ramped systems: the compost-bomb instability
- Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions
- Pattern and Waves for a Model in Population Dynamics with Nonlocal Consumption of Resources
- Traveling Pulse Solutions for the Discrete FitzHugh–Nagumo System
- Reduction of quasilinear elliptic equations in cylindrical domains with applications
- Pattern formation in the one-dimensional Gray - Scott model
- Existence and persistence of invariant manifolds for semiflows in Banach space
- One-Parameter Semigroups for Linear Evolution Equations
- Patterned vegetation, tipping points, and the rate of climate change
- Spot Dynamics in a Reaction-Diffusion Model of Plant Root Hair Initiation
- Center manifolds without a phase space
- Ducks in space: from nonlinear absolute instability to noise-sustained structures in a pattern-forming system
- Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
- Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction–diffusion equations
- The Slow Passage through a Hopf Bifurcation: Delay, Memory Effects, and Resonance
- Relaxation oscillations including a standard chase on French ducks
- Canard cycles and center manifolds
- Stability of pulse solutions for the discrete FitzHugh–Nagumo system
- Geometric Singular Perturbation Theory Beyond the Standard Form
- A New Resonance Mechanism in the Swift--Hohenberg Equation with Time-Periodic Forcing
- Stripe to Spot Transition in a Plant Root Hair Initiation Model
- Theoretical Numerical Analysis
- Transonic canards and stellar wind
- Neural Fields
- Canard Theory and Excitability
- Continuation of Localized Coherent Structures in Nonlocal Neural Field Equations
- Elliptic Partial Differential Equations
- Relaxation oscillation and canard explosion
- Canards in \(\mathbb{R}^3\)
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Local Theory for Spatio-Temporal Canards and Delayed Bifurcations