Limit cycles in uniform isochronous centers of discontinuous differential systems with four zones

DOI10.3934/dcdsb.2017136zbMath1371.34029OpenAlexW2609736742MaRDI QIDQ2364734

Jackson Itikawa, Jaume Llibre, Ana Cristina Mereu, Regilene D. S. Oliveira

Publication date: 25 July 2017

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

Full work available at URL: https://doi.org/10.3934/dcdsb.2017136

zbMATH Keywords

limit cycleaveraging theoryuniform isochronous centerdiscontinuous polynomial system

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (9)

Limit cycles appearing from the perturbation of differential systems with multiple switching curves ⋮ A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system ⋮ ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION ⋮ Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system ⋮ Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems ⋮ Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations ⋮ Limit cycle bifurcations from a quadratic center with two switching lines ⋮ Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines ⋮ Limit Cycles on Piecewise Smooth Vector Fields with Coupled Rigid Centers

Cites Work

• On commuting vector fields and Darboux functions for planar differential equations
• The center-focus problem and small amplitude limit cycles in rigid systems
• Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
• Bifurcation of limit cycles from quadratic isochrones
• Limit cycles of differential equations
• Cubic systems and Abel equations
• Conditions for a centre in a simple class of cubic systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• A new result on averaging theory for a class of discontinuous planar differential systems with applications
• Limit cycles for rigid cubic systems
• Computing center conditions for vector fields with constant angular speed
• Linearization of isochronous centers
• Limit cycles for discontinuous quadratic differential systems with two zones
• Averaging theory for discontinuous piecewise differential systems
• Phase portraits of uniform isochronous quartic centers
• Piecewise-smooth dynamical systems. Theory and applications
• Geometry of the uniformly isochronous centers with polynomial commutator
• ON PLANAR AND NON-PLANAR ISOCHRONOUS SYSTEMS AND POISSON STRUCTURES
• Exact number of limit cycles for a family of rigid systems
• ON INTEGRABILITY OF DIFFERENTIAL EQUATIONS DEFINED BY THE SUM OF HOMOGENEOUS VECTOR FIELDS WITH DEGENERATE INFINITY
• Isochronous centers of cubic systems with degenerate infinity
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