BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
From MaRDI portal
Publication:3586852
DOI10.1142/S021812741002654XzbMath1193.34082OpenAlexW2046380677MaRDI QIDQ3586852
Publication date: 1 September 2010
Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1142/s021812741002654x
Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Discontinuous ordinary differential equations (34A36) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)
Related Items
Bifurcation of limit cycles for a perturbed piecewise quadratic differential systems, On the number of limit cycles in small perturbations of a piecewise linear Hamiltonian system with a heteroclinic loop, Limit cycles appearing from the perturbation of differential systems with multiple switching curves, An estimate of the number of limit cycles bifurcating from a planar integrable system, Bifurcation methods of periodic orbits for piecewise smooth systems, Twenty-Six Crossing Limit Cycles Around One Singular Point in a Cubic Switching System, Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system, The number of limit cycles from the perturbation of a quadratic isochronous system with two switching lines, The number of limit cycles by perturbing a piecewise linear system with three zones, The cyclicity of a class of global nilpotent center under perturbations of piecewise smooth polynomials with four zones, Bifurcation of periodic orbits emanated from a vertex in discontinuous planar systems, On the number of limit cycles of a pendulum-like equation with two switching lines, Limit Cycles Appearing From Piecewise Smooth Perturbations to a Reversible Nonlinear Center, Limit Cycles from Hopf Bifurcation in Nongeneric Quadratic Reversible Systems with Piecewise Perturbations, The Exact Bound of the Number of Limit Cycles Bifurcating from the Global Nilpotent Center with a Nonlinear Switching Curve, Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems, Limit Cycle Bifurcations by Perturbing a Piecewise Hamiltonian System with a Double Homoclinic Loop, On the Limit Cycles Bifurcating from Piecewise Quasi-Homogeneous Differential Center, On the number of limit cycles bifurcating from the linear center with an algebraic switching curve, Limit cycles of discontinuous perturbed quadratic center via the second order averaging method, Limit cycle bifurcations in a class of piecewise smooth cubic systems with multiple parameters, Up to second order Melnikov functions for general piecewise Hamiltonian systems with nonregular separation line, Bifurcation of periodic orbits by perturbing high-dimensional piecewise smooth integrable systems, Limit cycle bifurcations of a piecewise smooth Hamiltonian system with a generalized heteroclinic loop through a cusp, Limit Cycles Bifurcating from a Periodic Annulus in Discontinuous Planar Piecewise Linear Hamiltonian Differential System with Three Zones, Bifurcation from Periodic Orbits of n-Dimensional Piecewise Smooth Differential Systems with Two Switching Planes, Hopf bifurcation of limit cycles by perturbing piecewise integrable systems, Bifurcation of periodic orbits with multiple crossings in a class of planar Filippov systems, On the Number of Limit Cycles by Perturbing a Piecewise Smooth Liénard Model, Limit Cycles for a Class of Piecewise Smooth Quadratic Differential Systems with Multiple Parameters, Limit Cycle Bifurcations for Piecewise Smooth Hamiltonian Systems with a Generalized Eye-Figure Loop, A linear estimate of the number of limit cycles for a piecewise smooth near-Hamiltonian system, The existence and stability analyses of periodic orbits in 3-dimensional piecewise affine systems, Limit cycle bifurcations of near-Hamiltonian systems with multiple switching curves and applications, Bifurcation of Limit Cycles from a Class of Piecewise Smooth Systems with Two Vertical Straight Lines of Singularity, Bifurcation of Nonhyperbolic Limit Cycles in Piecewise Smooth Planar Systems with Finitely Many Zones, The number of limit cycles of a kind of piecewise quadratic systems with switching curve \(y = x^m\), The limit cycle bifurcations of a whirling pendulum with piecewise smooth perturbations, The Maximal Number of Limit Cycles in Perturbations of Piecewise Linear Hamiltonian Systems with Two Saddles, Bifurcation of limit cycles of the nongeneric quadratic reversible system with discontinuous perturbations, Bifurcations of limit cycles in piecewise smooth Hamiltonian system with boundary perturbation, Heteroclinic loop bifurcations by perturbing a class of \(\mathrm{Z}_2\)-equivariant quadratic switching Hamiltonian systems with nilpotent singular points, Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations, Bifurcation of Limit Cycles in a 12-Degree Hamiltonian System Under Thirteenth-Order Perturbation, Existence of Homoclinic Cycles and Periodic Orbits in a Class of Three-Dimensional Piecewise Affine Systems, Bifurcation Analysis in a Class of Piecewise Nonlinear Systems with a Nonsmooth Heteroclinic Loop, BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION, On the number of limit cycles of a piecewise quadratic near-Hamiltonian system, Bifurcation of limit cycles in a family of piecewise smooth systems via averaging theory, The Cyclicity of Period Annulus of Degenerate Quadratic Hamiltonian Systems with Polycycles S(2) or S(3) Under Perturbations of Piecewise Smooth Polynomials, Bifurcation of a Kind of Piecewise Smooth Generalized Abel Equation via First and Second Order Analyses, On the limit cycles of perturbed discontinuous planar systems with 4 switching lines, Limit cycles bifurcating from piecewise quadratic systems separated by a straight line, Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials, Melnikov functions and limit cycles in piecewise smooth perturbations of a linear center using regularization method, Limit cycle bifurcations for piecewise smooth integrable differential systems, ON THE NUMBER OF LIMIT CYCLES BY PERTURBING A PIECEWISE SMOOTH HAMILTON SYSTEM WITH TWO STRAIGHT LINES OF SEPARATION, Limit Cycles Near a Piecewise Smooth Generalized Homoclinic Loop with a Nonelementary Singular Point, Higher order Melnikov analysis for planar piecewise linear vector fields with nonlinear switching curve, Unnamed Item, On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials, Limit cycle bifurcations of piecewise smooth near-Hamiltonian systems with a switching curve, On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \), A class of reversible quadratic systems with piecewise polynomial perturbations, Limit Cycles of a Class of Piecewise Smooth Liénard Systems, Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system, Bifurcation of limit cycles by perturbing a piecewise linear Hamiltonian system, On the number of limit cycles for a class of piecewise smooth Hamiltonian systems with discontinuous perturbations, Limit cycles by perturbing quadratic isochronous centers inside piecewise polynomial differential systems, Limit Cycles from Perturbing a Piecewise Smooth System with a Center and a Homoclinic Loop, FURTHER STUDIES ON LIMIT CYCLE BIFURCATIONS FOR PIECEWISE SMOOTH NEAR-HAMILTONIAN SYSTEMS WITH MULTIPLE PARAMETERS<inline-formula><tex-math id="M1">$ ^* $</tex-math></inline-formula>, Limit cycles in two kinds of quadratic reversible systems with non-smooth perturbations, Bifurcation of limit cycles in a piecewise smooth near-integrable system, Limit cycle bifurcations from a quadratic center with two switching lines, The dynamics of a kind of Liénard system with sixth degree and its limit cycle bifurcations under perturbations, Second Order Melnikov Functions of Piecewise Hamiltonian Systems, Picard–Fuchs Equation Applied to Quadratic Isochronous Systems with Two Switching Lines, Bifurcation of Periodic Orbits Crossing Switching Manifolds Multiple Times in Planar Piecewise Smooth Systems, Limit Cycle Bifurcations Near a Piecewise Smooth Generalized Homoclinic Loop with a Saddle-Fold Point, Melnikov functions of arbitrary order for piecewise smooth differential systems in \(\mathbb{R}^n\) and applications, Limit Cycles of Planar Piecewise Smooth Quadratic Systems with Focus-Parabolic Type Critical Points, Limit Cycles of a Kind of Nonsmooth Differential Systems with Two Switching Lines, Limit cycles in piecewise polynomial systems allowing a non-regular switching boundary, Bifurcation of limit cycles of a piecewise smooth Hamiltonian system, Limit cycle bifurcations by perturbing piecewise Hamiltonian systems with a nonregular switching line via multiple parameters, Further study on Horozov-Iliev's method of estimating the number of limit cycles, Number of Limit Cycles from a Class of Perturbed Piecewise Polynomial Systems, LIMIT CYCLE BIFURCATIONS IN DISCONTINUOUS PLANAR SYSTEMS WITH MULTIPLE LINES, Limit cycles in piecewise polynomial Hamiltonian systems allowing nonlinear switching boundaries, A new Chebyshev criterion and its application to planar differential systems, Limit Cycle Bifurcations in a Class of Piecewise Smooth Polynomial Systems, Persistence of periodic solutions from discontinuous planar piecewise linear Hamiltonian differential systems with three zones, A linear estimate of the number of limit cycles for some planar piecewise smooth quadratic differential system, Limit cycle bifurcations in a planar piecewise quadratic system with multiple parameters, Limit cycle bifurcations near generalized homoclinic loop in piecewise smooth differential systems
Cites Work
- Bifurcation of periodic orbits in a class of planar Filippov systems
- On Hopf cyclicity of planar systems
- Planar systems of piecewise linear differential equations with a line of discontinuity
- On the existence and uniqueness of limit cycles in Liénard differential equations allowing discontinuities
- Bifurcations of Nonlinear Oscillations and Frequency Entrainment Near Resonance
- Center-Focus Problem for Discontinuous Planar Differential Equations
- ON THE NUMBER OF LIMIT CYCLES IN PIECEWISE-LINEAR LIÉNARD SYSTEMS
- The Hopf cyclicity of Lienard systems
