BIFURCATIONS OF RELAXATION OSCILLATIONS NEAR FOLDED SADDLES

DOI10.1142/S0218127405014131zbMath1140.34368OpenAlexW2020906290MaRDI QIDQ5474354

John Guckenheimer, Kathleen A. Hoffman, Warren Weckesser

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0218127405014131

Mathematics Subject Classification ID

Singular perturbations for ordinary differential equations (34E15) Local and nonlocal bifurcation theory for dynamical systems (37G99) Relaxation oscillations for ordinary differential equations (34C26)

Related Items (9)

Attractors of harmonically forced linear oscillator with attached nonlinear energy sink. I: Description of response regimes ⋮ Stability and oscillations in a slow-fast flexible joint system with transformation delay ⋮ Canard Cycles and Relaxation Oscillations in a Singularly Perturbed Leslie–Gower Predator–Prey Model with Allee Effect ⋮ Slow-fast \(n\)-dimensional piecewise linear differential systems ⋮ Canards in Stiction: On Solutions of a Friction Oscillator by Regularization ⋮ A Stiction Oscillator with Canards: On Piecewise Smooth Nonuniqueness and Its Resolution by Regularization Using Geometric Singular Perturbation Theory ⋮ Strongly modulated response in forced 2DOF oscillatory system with essential mass and potential asymmetry ⋮ Bifurcations of self-excitation regimes in a Van der Pol oscillator with a nonlinear energy sink ⋮ Weakly Nonlinear Liquid Sloshing: Modelling and Exploration of Response Regimes

Uses Software

• AUTO

Cites Work

• Duck-shaped solutions and winding.
• The Forced van der Pol Equation II: Canards in the Reduced System
• Existence and Bifurcation of Canards in $\mathbbR^3$ in the Case of a Folded Node
• The Forced van der Pol Equation I: The Slow Flow and Its Bifurcations
• A CONTRIBUTION TO THE PROBLEM OF THE STRUCTURE OF AN EXTENDED NEIGHBORHOOD OF A ROUGH EQUILIBRIUM STATE OF SADDLE-FOCUS TYPE
• Canards in \(\mathbb{R}^3\)

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