Systematic derivation of amplitude equations and normal forms for dynamical systems

DOI10.1063/1.166370zbMath0987.37074arXivchao-dyn/9803006OpenAlexW1978484756WikidataQ52015429 ScholiaQ52015429MaRDI QIDQ4515084

Mads Ipsen, Preben Graae Sørensen, F. Hynne

Publication date: 12 November 2000

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

Full work available at URL: https://arxiv.org/abs/chao-dyn/9803006

zbMATH Keywords

normal formsrecurrence relationdiscrete dynamicsflowslocal bifurcationscenter manifoldamplitude equations

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Dynamics induced by flows and semiflows (37C10) Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10)

Related Items (6)

Spatio-temporal organization in a morphochemical electrodeposition model: analysis and numerical simulation of spiral waves ⋮ Amplitude equations for reaction-diffusion systems with a Hopf bifurcation and slow real modes ⋮ Global Hopf bifurcation in the ZIP regulatory system ⋮ Sinusoidal-signal detection by active, noisy oscillators on the brink of self-oscillation ⋮ Switching to nonhyperbolic cycles from codim 2 bifurcations of equilibria in ODEs ⋮ Amplitude equations for description of chemical reaction-diffusion systems

Cites Work

• A two-dimensional mapping with a strange attractor
• A simple global characterization for normal forms of singular vector fields
• Determination of invariant tori bifurcation points
• On the non-linear mechanics of wave disturbances in stable and unstable parallel flows Part 1. The basic behaviour in plane Poiseuille flow
• Amplitude Equations for Systems with Competing Instabilities
• Amplitude Equations and Chemical Reaction–Diffusion Systems
• Deterministic Nonperiodic Flow

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