Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction–diffusion equations

DOI10.1063/1.5050508zbMath1397.35137OpenAlexW2894346931WikidataQ57120328 ScholiaQ57120328MaRDI QIDQ4689225

Tasso J. Kaper, Theodore Vo

Publication date: 15 October 2018

Published in: Chaos: An Interdisciplinary Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.5050508

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Reaction-diffusion equations (35K57) Bifurcations in context of PDEs (35B32)

Related Items (8)

Pattern formation in a spatially extended model of pacemaker dynamics in smooth muscle cells ⋮ A survey on the blow-up method for fast-slow systems ⋮ Complex bursting dynamics in the cubic-quintic Duffing-van der Pol system with two external periodic excitations ⋮ Local Theory for Spatio-Temporal Canards and Delayed Bifurcations ⋮ Competition instabilities of spike patterns for the 1D Gierer–Meinhardt and Schnakenberg models are subcritical ⋮ Complex mixed-mode vibration types triggered by the pitchfork bifurcation delay in a driven van der Pol-Duffing oscillator ⋮ Andronov-Hopf and Neimark-Sacker bifurcations in time-delay differential equations and difference equations with applications to models for diseases and animal populations ⋮ Stability and Hopf bifurcation of a predator-prey model

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Geometric desingularization of degenerate singularities in the presence of fast rotation: A new proof of known results for slow passage through Hopf bifurcations
• Bifurcations of canard-induced mixed mode oscillations in a pituitary lactotroph model
• Delayed oscillation phenomena in the FitzHugh Nagumo equation
• Chemical oscillations, waves, and turbulence
• A Hodgkin-Huxley model exhibiting bursting oscillations
• Mathematical physiology. II: Systems physiology
• Mathematical foundations of neuroscience
• On delayed oscillation in nonspatially uniform FitzHugh Nagumo equation
• Topological and phenomenological classification of bursting oscillations
• Two-dimensional localized structures in harmonically forced oscillatory systems
• Slowly varying control parameters, delayed bifurcations, and the stability of spikes in reaction-diffusion systems
• Mixed mode oscillations as a mechanism for pseudo-plateau bursting
• Synchronization of Elliptic Bursters
• An Introduction to Modeling Neuronal Dynamics
• The world of the complex Ginzburg-Landau equation
• Slow Passage Through a Hopf Bifurcation: From Oscillatory to Steady State Solutions
• Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
• The Slow Passage through a Hopf Bifurcation: Delay, Memory Effects, and Resonance
• Operator Splitting
• Balanced Splitting and Rebalanced Splitting
• A-Type K⁺ Current Can Act as a Trigger for Bursting in the Absence of a Slow Variable

This page was built for publication: Delayed loss of stability due to the slow passage through Hopf bifurcations in reaction–diffusion equations