Small-scale instabilities in dynamical systems with sliding

DOI10.1016/j.physd.2009.10.003zbMath1203.37088arXiv0811.1944OpenAlexW2005065697WikidataQ57940465 ScholiaQ57940465MaRDI QIDQ979087

Jan Sieber, Piotr Kowalczyk

Publication date: 25 June 2010

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0811.1944

zbMATH Keywords

Filippov systems, grazing-sliding bifurcation, discontinuity induced bifurcationstable singular perturbation

Mathematics Subject Classification ID

Singular perturbations of ordinary differential equations (34D15) Discontinuous ordinary differential equations (34A36) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Singular perturbations for ordinary differential equations (34E15)

Related Items (11)

Hidden dynamics in models of discontinuity and switching ⋮ Period-adding and the Farey tree structure in a class of one-dimensional discontinuous nonlinear maps ⋮ Dimension reduction for slow-fast, piecewise-linear ODEs and obstacles to a general theory ⋮ Piecewise-smooth slow-fast systems ⋮ Smoothing tautologies, hidden dynamics, and sigmoid asymptotics for piecewise smooth systems ⋮ Persistence of periodic orbits with sliding or sewing by singular perturbation ⋮ Rosenbrock-type methods applied to discontinuous differential systems ⋮ Stochastic perturbations of periodic orbits with sliding ⋮ Nonsmooth frameworks for an extended Budyko model ⋮ Model reduction of non-densely defined piecewise-smooth systems in Banach spaces ⋮ Boundary-equilibrium bifurcations in piecewise-smooth slow-fast systems

Cites Work

• Period increment cascades in a discontinuous map with square-root singularity
• Geometric singular perturbation theory for ordinary differential equations
• Grazing bifurcations and basins of attraction in an impact-friction oscillator
• Oscillations in a second-order discontinuous system with delay.
• Piecewise-smooth dynamical systems. Theory and applications
• Bifurcation analysis of piecewise smooth ecological models
• Slow periodic motions with internal sliding modes in variable structure systems
• Singularly perturbed analysis of chattering in relay control systems
• Explicit periodic solutions in a model of a relay controller with delay and forcing

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