Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones

DOI10.1007/s00033-016-0642-2zbMath1362.34026OpenAlexW2335839603MaRDI QIDQ322092

Zhengdong Du, Jun Shen

Publication date: 14 October 2016

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-016-0642-2

zbMATH Keywords

chaotic behaviourheteroclinic orbitsMelnikov methodpiecewise smooth systems

Mathematics Subject Classification ID

Theoretical approximation of solutions to ordinary differential equations (34A45) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Complex behavior and chaotic systems of ordinary differential equations (34C28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (9)

Limit cycles appearing from the perturbation of differential systems with multiple switching curves ⋮ Stability and perturbations of generalized heteroclinic loops in piecewise smooth systems ⋮ Bifurcation of periodic orbits in discontinuous systems ⋮ Chaos of the Rayleigh-Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation ⋮ Impact limit cycles in the planar piecewise linear hybrid systems ⋮ Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations ⋮ Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations ⋮ Limit cycle bifurcations from a quadratic center with two switching lines ⋮ Bifurcations of a generalized heteroclinic loop in a planar piecewise smooth system with periodic perturbations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Mel'nikov methods and homoclinic orbits in discontinuous systems
• Homoclinic bifurcation in a quasiperiodically excited impact inverted pendulum
• Bifurcations of planar sliding homoclinics
• Bifurcation and chaos in discontinuous and continuous systems
• An example of chaotic behaviour in presence of a sliding homoclinic orbit
• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
• Melnikov method for discontinuous planar systems
• Homoclinic trajectories in discontinuous systems
• Bifurcation and chaos near sliding homoclinics
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Bifurcations of subharmonics
• The transition to chaos in a simple mechanical system
• An example of bifurcation to homoclinic orbits
• Global bifurcations and chaos. Analytical methods
• Non-smooth dynamical systems
• Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
• Chaos in forced impact systems
• Melnikov theory for a class of planar hybrid systems
• Impact oscillators with homoclinic orbit tangent to the wall
• Piecewise-smooth dynamical systems. Theory and applications
• Melnikov method and detection of chaos for non-smooth systems
• The scattering map in two coupled piecewise-smooth systems, with numerical application to rocking blocks
• Topological Degree Approach to Bifurcation Problems
• Heteroclinic Orbits and Chaotic Dynamics in Planar Fluid Flows
• Heteroclinic bifurcations in damped rigid block motion
• Heteroclinic Bifurcations and Invariant Manifolds in Rocking Block Dynamics
• The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System
• Bifurcation for Non-smooth Dynamical Systems via Reduction Methods
• An Algorithm for Melnikov Functions and Application to a Chaotic Rotor
• HETEROCLINIC BIFURCATIONS AND OPTIMAL CONTROL IN THE NONLINEAR ROCKING DYNAMICS OF GENERIC AND SLENDER RIGID BLOCKS

This page was built for publication: Heteroclinic bifurcation in a class of planar piecewise smooth systems with multiple zones