The third order melnikov function of a cubic integrable system under quadratic perturbations

被引：5

作者：

Asheghi, R. ^{[1
]}

Nabavi, A. ^{[1
]}

机构：

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

来源：

CHAOS SOLITONS & FRACTALS | 2020年 / 139卷

关键词：

Melnikov functions; Integrable system; Quadratic perturbations; Limit cycles; Reversible; LIMIT-CYCLES;

D O I：

10.1016/j.chaos.2020.110291

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this work, we consider a cubic integrable system under quadratic perturbations. We then study the limit cycles of the perturbed system by using Melnikov functions up to order three. We prove that the sharp upper bound of the number of limit cycles lies between six and seven. Also, we give an example that shows six limit cycles. (C) 2020 Elsevier Ltd. All rights reserved.

引用

页数：9

共 50 条

[21] LIMIT CYCLES FOR QUADRATIC AND CUBIC PLANAR DIFFERENTIAL EQUATIONS UNDER POLYNOMIAL PERTURBATIONS OF SMALL DEGREE
Martins, Ricardo M.
Gomide, Otavio M. L.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2017, 37 (06) : 3353 - 3386
[22] Bifurcations of limit cycles for a cubic Hamiltonian system under quartic perturbations
Zhang, TH
Han, MA
Zang, H
Meng, XZ
CHAOS SOLITONS & FRACTALS, 2004, 22 (05) : 1127 - 1138
[23] RAPID DETERMINATION OF A COMPENSATOR AND RESPONSE OF A THIRD ORDER SYSTEM IN QUADRATIC OPTIMALIZATION
HUMBERT, C
AUBRUN, M
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES SERIE A, 1969, 269 (25): : 1230 - &
[24] The Abelian integrals of a one-parameter Hamiltonian system under cubic perturbations
Zhang, TH
Chen, WC
Hong, Z
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2004, 14 (05): : 1853 - 1862
[25] The Abelian Integrals of a Class of Non-Hamiltonian System under Cubic Perturbations
Qi, Xiaomei
Chen, Wencheng
PROCEEDINGS OF THE 6TH CONFERENCE OF BIOMATHEMATICS, VOLS I AND II: ADVANCES ON BIOMATHEMATICS, 2008, : 603 - 606
[26] Centers in a Quadratic System Obtained from a Scalar Third Order Differential Equation
Buica, Adriana
Garcia, Isaac A.
Maza, Susanna
DIFFERENTIAL AND DIFFERENCE EQUATIONS WITH APPLICATI ONS, 2013, 47 : 405 - 410
[27] ANALYSIS OF A QUADRATIC SYSTEM OBTAINED FROM A SCALAR THIRD ORDER DIFFERENTIAL EQUATION
Dias, Fabio Scalco
Mello, Luis Fernando
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2010,
[28] Cubic splines method for a system of third-order boundary value problems
Al-Said, EA
Noor, MA
APPLIED MATHEMATICS AND COMPUTATION, 2003, 142 (2-3) : 195 - 204
[29] Discussion on localized pulses for third-order nonlinear Schrodinger equation and negative index material with quadratic cubic nonlinearity
Rizvi, Syed T. R.
Seadawy, Aly R.
Shabbir, S.
Khizar, S.
Mustafa, B.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2024, 38 (05):
[30] Analysis of chaos behaviors of a bistable piezoelectric cantilever power generation system by the second-order Melnikov function
Shu Sun
Shu-Qian Cao
Acta Mechanica Sinica, 2017, 33 : 200 - 207

← 1 2 3 4 5 →