Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory

DOI10.3934/dcdss.2020133zbMath1479.37050OpenAlexW2991246765WikidataQ126641207 ScholiaQ126641207MaRDI QIDQ2230311

Shanshan Liu, Mao'an Han

Publication date: 17 September 2021

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdss.2020133

zbMATH Keywords

averaging methodlimit cycle bifurcationpiecewise Hamiltonian systems

Mathematics Subject Classification ID

Averaging method for ordinary differential equations (34C29) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (5)

Bifurcation methods of periodic orbits for piecewise smooth systems ⋮ The number of limit cycles for some polynomial systems with multiple parameters ⋮ Bifurcation of limit cycles in a piecewise smooth near-integrable system ⋮ Limit cycles of piecewise polynomial differential systems with the discontinuity line \(xy = 0\) ⋮ Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary

Cites Work

• Limit cycle bifurcations in a class of perturbed piecewise smooth systems
• On the number of limit cycles for a class of discontinuous quadratic differential systems
• Limit cycle bifurcations for piecewise smooth integrable differential systems
• Normal forms, Melnikov functions and bifurcations of limit cycles
• A new result on averaging theory for a class of discontinuous planar differential systems with applications
• Bifurcation theory for finitely smooth planar autonomous differential systems
• Averaging theory at any order for computing limit cycles of discontinuous piecewise differential systems with many zones
• On the birth of limit cycles for non-smooth dynamical systems
• Limit cycles for discontinuous quadratic differential systems with two zones
• Averaging theory for discontinuous piecewise differential systems
• Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems
• Equivalence of the Melnikov function method and the averaging method
• ON THE NUMBER OF LIMIT CYCLES IN NEAR-HAMILTONIAN POLYNOMIAL SYSTEMS
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• Bifurcation of Limit Cycles from the Center of a Family of Cubic Polynomial Vector Fields
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION
• ON THE MAXIMUM NUMBER OF PERIODIC SOLUTIONS OF PIECEWISE SMOOTH PERIODIC EQUATIONS BY AVERAGE METHOD
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