Melnikov Method for a Class of Planar Hybrid Piecewise-Smooth Systems

DOI10.1142/S0218127416500309zbMath1334.34037OpenAlexW2294518167MaRDI QIDQ2800722

Shuangbao Li, Wensai Ma, Wei Zhang, Yuxin Hao

Publication date: 18 April 2016

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

Full work available at URL: https://doi.org/10.1142/s0218127416500309

zbMATH Keywords

homoclinic bifurcationsMelnikov methodswitching manifoldplanar hybrid piecewise-smooth systemschaotic boundariespiecewise-smooth homoclinic solutions

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Complex behavior and chaotic systems of ordinary differential equations (34C28) Invariant manifolds for ordinary differential equations (34C45) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (9)

The Melnikov method of heteroclinic orbits for a class of planar hybrid piecewise-smooth systems and application ⋮ Melnikov-type method for chaos in a class of hybrid piecewise-smooth systems with impact and noise excitation under unilateral rigid constraint ⋮ Global dynamics for a class of tristable system with negative stiffness ⋮ Chaotic behavior of driven, second-order, piecewise linear systems ⋮ Random Disordered Periodical Input Induced Chaos in Discontinuous Systems ⋮ The Melnikov method for detecting chaotic dynamics in a planar hybrid piecewise-smooth system with a switching manifold ⋮ Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator ⋮ Lateral Dynamics of Walking-Like Mechanical Systems and Their Chaotic Behavior ⋮ Bursting Oscillations as well as the Mechanism in a Filippov System with Parametric and External Excitations

Cites Work

• Unnamed Item
• Mel'nikov methods and homoclinic orbits in discontinuous systems
• Melnikov method for homoclinic bifurcation in nonlinear impact oscillators
• Melnikov method for discontinuous planar systems
• Bifurcation of periodic orbits in a class of planar Filippov systems
• Bifurcation and chaos near sliding homoclinics
• Nonsmooth mechanics. Models, dynamics and control.
• Melnikov theory for a class of planar hybrid systems
• Piecewise-smooth dynamical systems. Theory and applications
• SLIDING BIFURCATIONS: A NOVEL MECHANISM FOR THE SUDDEN ONSET OF CHAOS IN DRY FRICTION OSCILLATORS
• Bifurcations in piecewise-smooth feedback systems
• The Melnikov Method and Subharmonic Orbits in a Piecewise-Smooth System
• Melnikov-Type Method for a Class of Discontinuous Planar Systems and Applications
• Bifurcations in nonlinear discontinuous systems

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