Melnikov Method for a Three-Zonal Planar Hybrid Piecewise-Smooth System and Application

DOI10.1142/S0218127416500140zbMath1334.34036OpenAlexW2274813661MaRDI QIDQ2800700

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/s0218127416500140

zbMATH Keywords

periodic orbitsPoincaré mapMelnikov methodplanar hybrid piecewise-smooth systemsswitching manifolds

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Perturbations of ordinary differential equations (34D10) Discontinuous ordinary differential equations (34A36)

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The Melnikov method of heteroclinic orbits for a class of planar hybrid piecewise-smooth systems and application ⋮ Suppressing homoclinic chaos for a weak periodically excited non-smooth oscillator ⋮ Bursting Oscillations as well as the Mechanism in a Filippov System with Parametric and External Excitations ⋮ Chaotic threshold of a class of hybrid piecewise-smooth system by an impulsive effect via Melnikov-type function ⋮ Chaotic motion and control of the driven-damped double sine-Gordon equation ⋮ Bifurcation of periodic orbits and its application for high-dimensional piecewise smooth near integrable systems with two switching manifolds

Cites Work

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• Asymptotic Stability of Periodic Solutions for Nonsmooth Differential Equations with Application to the Nonsmooth van der Pol Oscillator
• 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
• Limit cycles of some polynomial differential systems in dimension 2, 3 and 4, via averaging theory

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