Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations

DOI10.1016/j.jde.2018.01.017zbMath1390.34082OpenAlexW2791133188MaRDI QIDQ1701860

Jihua Yang, Lincheng Zhao

Publication date: 27 February 2018

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2018.01.017

zbMATH Keywords

limit cyclediscontinuous differential systempiecewise smooth differential systemPicard--Fuchs equation

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Discontinuous ordinary differential equations (34A36) Perturbations, asymptotics of solutions to ordinary differential equations (34E10)

Related Items (24)

Limit cycles appearing from the perturbation of differential systems with multiple switching curves ⋮ Bifurcation methods of periodic orbits for piecewise smooth systems ⋮ The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines ⋮ The Exact Bound of the Number of Limit Cycles Bifurcating from the Global Nilpotent Center with a Nonlinear Switching Curve ⋮ On the number of limit cycles bifurcating from the linear center with an algebraic switching curve ⋮ Bifurcation from Periodic Orbits of n-Dimensional Piecewise Smooth Differential Systems with Two Switching Planes ⋮ A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system ⋮ The number of limit cycles of a kind of piecewise quadratic systems with switching curve \(y = x^m\) ⋮ Phase portraits of continuous piecewise linear Liénard differential systems with three zones ⋮ Limit cycle bifurcations in perturbations of a reversible quadratic system with a non-rational first integral ⋮ The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials ⋮ Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials ⋮ On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials ⋮ A class of reversible quadratic systems with piecewise polynomial perturbations ⋮ Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system ⋮ Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations ⋮ Limit cycle bifurcations from a quadratic center with two switching lines ⋮ Perturbation of a period annulus bounded by a saddle-saddle cycle in a hyperelliptic Hamiltonian systems of degree seven ⋮ Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines ⋮ Periodic orbits for double regularization of piecewise smooth systems with a switching manifold of codimension two ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system ⋮ Further study on Horozov-Iliev's method of estimating the number of limit cycles ⋮ Global Analysis of an Asymmetric Continuous Piecewise Linear Differential System with Three Linear Zones ⋮ The Number of Zeros of Abelian Integral for a Quintic Hamiltonian Systems With a Rose-Figure Loop

Cites Work

• Unnamed Item
• Unnamed Item
• Bounding the number of zeros of certain abelian integrals
• Bifurcation of limit cycles from quadratic isochrones
• Perturbations of quadratic centers of genus one
• Limit cycles for discontinuous quadratic differential systems with two zones
• On the abelian integrals of quadratic reversible centers with orbits formed by genus one curves of higher degree
• Piecewise-smooth dynamical systems. Theory and applications
• Estimating the Number of Zeros for Abelian Integrals of Quadratic Reversible Centers with Orbits Formed by Higher-Order Curves
• Bifurcation of critical periods from Pleshkan's isochrones
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• 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
• On the Gause predator-prey model with a refuge: a fresh look at the history

This page was built for publication: Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations