Saddle-node bifurcation of invariant cones in 3D piecewise linear systems

DOI10.1016/j.physd.2011.11.020zbMath1252.34044OpenAlexW2049542748MaRDI QIDQ2428014

Victoriano Carmona, Soledad Fernández-García, Emilio Freire

Publication date: 19 April 2012

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

Full work available at URL: https://doi.org/10.1016/j.physd.2011.11.020

zbMATH Keywords

saddle-node bifurcationperiodic orbitshybrid systemsinvariant manifoldspiecewise linear systemsMelnikov functions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Perturbations of ordinary differential equations (34D10) Bifurcations of singular points in dynamical systems (37G10) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Invariant manifolds for ordinary differential equations (34C45)

Related Items

The instantaneous local transition of a stable equilibrium to a chaotic attractor in piecewise-smooth systems of differential equations ⋮ Twenty Hopf-like bifurcations in piecewise-smooth dynamical systems ⋮ Dimension reduction for slow-fast, piecewise-linear ODEs and obstacles to a general theory ⋮ Pseudo-Bautin Bifurcation in 3D Filippov Systems ⋮ Bifurcation of limit cycles in piecewise-smooth systems with intersecting discontinuity surfaces ⋮ Melnikov theory for a class of planar hybrid systems ⋮ Existence and Stability of Invariant Cones in 3-Dim Homogeneous Piecewise Linear Systems with Two Zones ⋮ Bifurcations in four-dimensional switched systems ⋮ Bifurcations from a center at infinity in 3D piecewise linear systems with two zones ⋮ Periodic orbits and invariant cones in three-dimensional piecewise linear systems ⋮ Invariant manifolds for nonsmooth systems with sliding mode ⋮ The number and stability of limit cycles for planar piecewise linear systems of node-saddle type ⋮ On the Number of Invariant Cones and Existence of Periodic Orbits in 3-dim Discontinuous Piecewise Linear Systems ⋮ Existence of Invariant Cones in General 3-Dim Homogeneous Piecewise Linear Differential Systems with Two Zones

Cites Work

• Unnamed Item
• Periodic orbits for perturbations of piecewise linear systems
• Reduction to invariant cones for non-smooth systems
• The continuous matching of two stable linear systems can be unstable
• Invariant cones for non-smooth dynamical systems
• Periodic solutions of homogeneous equations
• Hopf-like bifurcations in planar piecewise linear systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• Melnikov theory for a class of planar hybrid systems
• A method for proving the non-existence of limit cycles
• Piecewise-smooth dynamical systems. Theory and applications
• A BIPARAMETRIC BIFURCATION IN 3D CONTINUOUS PIECEWISE LINEAR SYSTEMS WITH TWO ZONES: APPLICATION TO CHUA'S CIRCUIT
• Pattern Formation in a Model of an Injured Nerve Fiber
• Corner-Impact Bifurcations: A Novel Class of Discontinuity-Induced Bifurcations in Cam-Follower Systems
• 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 Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• ON THE GENERALITY OF THE UNFOLDED CHUA'S CIRCUIT
• Computation of piecewise quadratic Lyapunov functions for hybrid systems
• One-Parameter Bifurcations in Planar Filippov Systems
• EXISTENCE OF POINCARÉ MAPS IN PIECEWISE LINEAR DIFFERENTIAL SYSTEMS IN ℝ^N
• Bifurcation Sets of Continuous Piecewise Linear Systems with Two Zones
• Existence of homoclinic connections in continuous piecewise linear systems
• On common quadratic lyapunov functions for pairs of stable lti systems whose system matrices are in companion form
• On simplifying and classifying piecewise-linear systems
• 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
• Regularization of kepler's problem and the averaging method on a manifold