Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems

DOI10.1007/s12346-014-0109-9zbMath1317.34040OpenAlexW1995669528MaRDI QIDQ489211

Jaume Llibre, Bruno D. Lopes, Jaime R. de Moraes

Publication date: 27 January 2015

Published in: Qualitative Theory of Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://ddd.uab.cat/record/150696

zbMATH Keywords

isochronous centerlimit cycleperiodic orbitaveraging methodpolynomial vector field

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) 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)

Related Items (15)

Eighteen limit cycles around two symmetric foci in a cubic planar switching polynomial system ⋮ Limit cycles for discontinuous quadratic differential switching systems ⋮ Existence and uniqueness of limit cycle in discontinuous planar differential systems ⋮ Bifurcation analysis on a class of \(Z_{2}\)-equivariant cubic switching systems showing eighteen limit cycles ⋮ Centers and isochronous centers of a class of quasi-analytic switching systems ⋮ Limit cycles in a class of switching system with a degenerate singular point ⋮ Bifurcation of limit cycles at infinity in a class of switching systems ⋮ On the limit cycles for continuous and discontinuous cubic differential systems ⋮ Center and isochronous center conditions for switching systems associated with elementary singular points ⋮ Bifurcation of limit cycles at infinity in piecewise polynomial systems ⋮ Limit cycles and invariant curves in a class of switching systems with degree four ⋮ Limit cycles for a discontinuous quintic polynomial differential system ⋮ On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials ⋮ Birth of limit cycles for a class of continuous and discontinuous differential systems in (d+ 2)–dimension ⋮ Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Phase portraits and invariant straight lines of cubic polynomial vector fields having a quadratic rational first integral
• Bifurcation of limit cycles from quadratic isochrones
• Limit cycles of cubic polynomial vector fields via the averaging theory
• Limit cycles of differential equations
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Nonlinear differential equations and dynamical systems
• Averaging methods for finding periodic orbits via Brouwer degree.
• On the shape of limit cycles that bifurcate from Hamiltonian centers
• Linear estimation of the number of zeros of abelian integral for some cubic isochronous centers
• Piecewise-smooth dynamical systems. Theory and applications
• The geometry of the real planar polynomial differential systems having their orbits embedded in conics
• Limit cycles of the generalized polynomial Liénard differential equations
• Bifurcation of Limit Cycles from Centers and Separatrix Cycles of Planar Analytic Systems
• On the nonexistence, existence and uniqueness of limit cycles
• Centennial History of Hilbert's 16th Problem
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• Averaging methods in nonlinear dynamical systems
• The shape of limit cycles that bifurcate from non-Hamiltonian centers
• Arbitrary order bifurcations for perturbed Hamiltonian planar systems via the reciprocal of an integrating factor

This page was built for publication: Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems