Smooth to discontinuous systems: a geometric and numerical method for slow-fast dynamics

DOI10.3934/dcdsb.2018112zbMath1398.65201OpenAlexW2790634078WikidataQ129474133 ScholiaQ129474133MaRDI QIDQ1670300

Cinzia Elia, Luca Dieci

Publication date: 5 September 2018

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2018112

zbMATH Keywords

slow-fast dynamicssliding motionrelaxation-oscillationexplicit Runge Kutta methodssystems with discontinuous right-hand side

Mathematics Subject Classification ID

Singular perturbations of ordinary differential equations (34D15) Discontinuous ordinary differential equations (34A36) Dynamical systems in numerical analysis (37N30) Numerical methods for ordinary differential equations (65L99)

Related Items (1)

Periodic orbits for double regularization of piecewise smooth systems with a switching manifold of codimension two

Cites Work

• A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side
• Dynamics of piecewise linear oscillators with van der Pol type damping
• A simplified model of coupled relaxation oscillators
• Canard-like phenomena in piecewise-smooth Van der Pol systems
• Qualitative analysis of the periodically forced relaxation oscillations
• A second order differential equation with singular solutions
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