PIECEWISE SMOOTH REVERSIBLE DYNAMICAL SYSTEMS AT A TWO-FOLD SINGULARITY

DOI10.1142/S0218127412501921zbMath1258.34069MaRDI QIDQ4907019

Durval José Tonon, Alain Jacquemard, Marco Antonio Teixeira

Publication date: 1 March 2013

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

zbMATH Keywords

structural stabilitysingularityreversibilitynonsmoothFilippov

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Symmetries, invariants of ordinary differential equations (34C14)

Related Items (16)

Asymptotic stability and bifurcations of 3D piecewise smooth vector fields ⋮ Piecewise smooth dynamical systems: persistence of periodic solutions and normal forms ⋮ Three Crossing Limit Cycles in a 3D-Filippov System Having a T-Singularity ⋮ Normal Forms for Codimension One Planar Piecewise Smooth Vector Fields ⋮ Periodic trajectories in planar discontinuous piecewise linear systems with only centers and with a nonregular switching line ⋮ Degenerate T-singularity bifurcation and crossing periodic orbits in a 3-dimensional piecewise smooth system ⋮ Study of Periodic Orbits in Periodic Perturbations of Planar Reversible Filippov Systems Having a Twofold Cycle ⋮ Hopf and homoclinic bifurcations on the sliding vector field of switching systems in \(\mathbb{R}^3\): a case study in power electronics ⋮ The chaotic behaviour of piecewise smooth differential equations on two-dimensional torus and sphere ⋮ Attractivity, degeneracy and codimension of a typical singularity in 3D piecewise smooth vector fields ⋮ Integration of a Dirac comb and the Bernoulli polynomials ⋮ Hopf-like bifurcations and asymptotic stability in a class of 3D piecewise linear systems with applications ⋮ Time switched differential equations and the Euler polynomials ⋮ Bifurcations at a degenerate two-fold singularity and crossing limit cycles ⋮ Piecewise smooth vector fields in \(\mathbb{R}^3\) at infinity ⋮ Fold bifurcation of T-singularities and invariant manifolds in 3D piecewise-smooth dynamical systems

Cites Work

• Teixeira singularities in 3D switched feedback control systems
• Time-reversal symmetry in dynamical systems: a survey
• Computer analysis of periodic orbits of discontinuous vector fields
• Stability conditions for discontinuous vector fields
• Nondeterministic Chaos, and the Two-fold Singularity in Piecewise Smooth Flows
• Topological Degree Approach to Bifurcation Problems
• The Two-Fold Singularity of Discontinuous Vector Fields
• Discontinuity geometry for an impact oscillator
• Invariant varieties of discontinuous vector fields
• One-Parameter Bifurcations in Planar Filippov Systems
• BIFURCATION ANALYSIS OF AN IMPACT MODEL FOR FOREST FIRE PREDICTION

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