The Ghosts of Departed Quantities in Switches and Transitions

DOI10.1137/15M1035756zbMath1387.34023arXiv1508.04344OpenAlexW2206872357MaRDI QIDQ3133145

Mike R. Jeffrey

Publication date: 13 February 2018

Published in: SIAM Review (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1508.04344

zbMATH Keywords

nonlinear dynamicsnon-uniquenessasymptotic seriesdiscontinuousFilippov's methodhidden terms

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Normal forms for dynamical systems (37G05) Bifurcations of singular points in dynamical systems (37G10) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Asymptotic expansions of solutions to ordinary differential equations (34E05)

Related Items (10)

Uncertainty in classical systems (with a local, non-stochastic, non-chaotic origin) ⋮ The discontinuous limit case of an archetypal oscillator with a constant excitation and van der Pol damping ⋮ Hidden Degeneracies in Piecewise Smooth Dynamical Systems ⋮ Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems ⋮ Nonlinear sliding and nonlinear regularization of piecewise smooth system ⋮ Novel slow-fast behaviour in an oscillator driven by a frequency-switching force ⋮ Ageing of an oscillator due to frequency switching ⋮ Sliding region and coexisting attractors of a friction-induced self-excited vibration ⋮ Micro-Slip as a Loss of Determinacy in Dry-Friction Oscillators ⋮ Pausing for arbitrarily long times in dynamical systems

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