On the number of limit cycles for generic Lotka-Volterra system and Bogdanov-Takens system under perturbations of piecewise smooth polynomials

DOI10.1016/j.nonrwa.2019.03.001zbMath1444.34056arXiv1805.10446OpenAlexW2963182088WikidataQ128207769 ScholiaQ128207769MaRDI QIDQ2283081

Shiyou Sui, Jihua Yang, Lincheng Zhao

Publication date: 27 December 2019

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1805.10446

zbMATH Keywords

limit cycleLotka-Volterra systemPicard-Fuchs equationBogdanov-Takens systemfirst-order Melnikov functionpiecewise smooth perturbation

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) 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) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items

Limit cycles appearing from the perturbation of differential systems with multiple switching curves ⋮ The cyclicity of a class of global nilpotent center under perturbations of piecewise smooth polynomials with four zones ⋮ The Exact Bound of the Number of Limit Cycles Bifurcating from the Global Nilpotent Center with a Nonlinear Switching Curve ⋮ Bifurcation analysis for energy transport system and its optimal control using parameter self-tuning law ⋮ On the number of limit cycles bifurcating from the linear center with an algebraic switching curve ⋮ Cyclicity of a Class of Hamiltonian Systems under Perturbations of Piecewise Smooth Polynomials ⋮ Bifurcation of limit cycles of a piecewise smooth Hamiltonian system

Cites Work

• Unnamed Item
• Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems
• Limit cycles for continuous and discontinuous perturbations of uniform isochronous cubic centers
• Limit cycles for a class of continuous and discontinuous cubic polynomial differential systems
• Limit cycle bifurcations for piecewise smooth integrable differential systems
• Quadratic perturbations of quadratic codimension-four centers
• Number of zeros of complete elliptic integrals
• The Chebyshev property of elliptic integrals
• Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
• Perturbations of quadratic centers
• Bounding the number of limit cycles of discontinuous differential systems by using Picard-Fuchs equations
• A note on a result of G. S. Petrov about the weakened 16th Hilbert problem
• Limit cycles for discontinuous quadratic differential systems with two zones
• Piecewise-smooth dynamical systems. Theory and applications
• Linear estimate on the number of zeros of Abelian integrals for quadratic centers having almost all their orbits formed by cubics
• BIFURCATION OF LIMIT CYCLES BY PERTURBING PIECEWISE HAMILTONIAN SYSTEMS
• HILBERT'S 16TH PROBLEM AND BIFURCATIONS OF PLANAR POLYNOMIAL VECTOR FIELDS
• BIFURCATION OF LIMIT CYCLES IN PIECEWISE SMOOTH SYSTEMS VIA MELNIKOV FUNCTION

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