Phantom ducks and models of excitability

DOI10.1007/BF01053807zbMath0762.34036MaRDI QIDQ1199671

Barteld Braaksma

Publication date: 16 January 1993

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

zbMATH Keywords

existencecomputationsasymptotic expansionsexcitabilityunstable manifoldblown-up equationfast fieldpantom duckssingular van der Pol equation

Mathematics Subject Classification ID

Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Qualitative theory for ordinary differential equations (34C99) Singular perturbations for ordinary differential equations (34E15)

Related Items (3)

Critical dynamics of the Bonhoeffer-van der Pol equation and its chaotic response to periodic stimulation ⋮ STOCHASTIC CHAOS IN A NEURONAL MODEL ⋮ Analytical approximation of the canard explosion in a van der Pol system with the nonlinear time transformation method

Cites Work

• The canard unchained or how fast/slow dynamical systems bifurcate
• On solutions of polynomial growth of ordinary differential equations
• Asymptotic methods for relaxation oscillations and applications
• Perturbation methods in applied mathematics
• Singular Hopf Bifurcation to Relaxation Oscillations
• Relaxation oscillations including a standard chase on French ducks
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