Periodic orbits for perturbations of piecewise linear systems

DOI10.1016/j.jde.2010.10.025zbMath1215.34012OpenAlexW2065261612MaRDI QIDQ627692

Emilio Freire, Victoriano Carmona, Soledad Fernández-García

Publication date: 3 March 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2010.10.025

zbMATH Keywords

periodic orbitsMelnikov functionaveraging methodinvariant manifoldpiecewise linear systems

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) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Discontinuous ordinary differential equations (34A36) Invariant manifolds for ordinary differential equations (34C45)

Related Items

Piecewise smooth dynamical systems: persistence of periodic solutions and normal forms ⋮ Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Bifurcation of piecewise smooth manifolds from 3D center-type vector fields ⋮ Saddle-node bifurcation of invariant cones in 3D piecewise linear systems ⋮ Quadratic stability and stabilization of bimodal piecewise linear systems ⋮ Limit cycles of continuous and discontinuous piecewise-linear differential systems in \(\mathbb{R}^3\) ⋮ Bifurcation of periodic orbits of a three-dimensional piecewise smooth system

Cites Work

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• Hopf-like bifurcations in planar piecewise linear systems
• Non-smooth dynamical systems
• The center problem for a family of systems of differential equations having a nilpotent singular point
• Geometric properties of the scattering map of a normally hyperbolic invariant manifold
• Algorithm of fast linear nonstationary stabilization and the Brockett problem
• A BIPARAMETRIC BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT
• Tangency Bifurcations of Global Poincaré Maps
• Existence of a Reversible T-Point Heteroclinic Cycle in a Piecewise Linear Version of the Michelson System
• Asymptotic Stability of Periodic Solutions for Nonsmooth Differential Equations with Application to the Nonsmooth van der Pol Oscillator
• The double scroll
• The ranges of transfer and return maps in three-region piecewise-linear dynamical systems
• Reality of chaos in the double scroll circuit: A computer-assisted proof
• Bifurcation of a periodic orbit from infinity in planar piecewise linear vector fields
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• ON THE GENERALITY OF THE UNFOLDED CHUA'S CIRCUIT
• EXISTENCE OF POINCARÉ MAPS IN PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ^N
• Invariant manifolds of periodic orbits for piecewise linear three-dimensional systems
• Existence of homoclinic connections in continuous piecewise linear systems
• On simplifying and classifying piecewise-linear systems
• Limit cycles of some polynomial differential systems in dimension 2, 3 and 4, via averaging theory
• LIMIT CYCLE BIFURCATION FROM CENTER IN SYMMETRIC PIECEWISE-LINEAR SYSTEMS
• BIFURCATION OF INVARIANT CONES IN PIECEWISE LINEAR HOMOGENEOUS SYSTEMS
• LIMIT CYCLE BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT
• Averaging methods in nonlinear dynamical systems
• Averaging analysis of a perturbated quadratic center