American Institute of Mathematical Sciences

Advanced
February  2010, 27(1): 325-335. doi: 10.3934/dcds.2010.27.325

Quadratic perturbations of a class of quadratic reversible systems with one center

Haihua Liang 1, and  Yulin Zhao 1,

1. 

Department of Mathematics, Sun Yat-Sen University, Guangzhou, 510275, China, China

Received  May 2009 Revised  September 2009 Published  February 2010

This paper is concerned with the bifurcation of limit cycles from a class of one-parameter family of quadratic reversible system under quadratic perturbations. The exact upper bound of the number of limit cycles is given.
Keywords: quadratic reversible system, Abelian integral., limit cycle, quadratic perturbations.
Mathematics Subject Classification: Primary: 34C07, 34C08; Secondary: 37G1.
Citation: Haihua Liang, Yulin Zhao. Quadratic perturbations of a class of quadratic reversible systems with one center. Discrete & Continuous Dynamical Systems - A, 2010, 27 (1) : 325-335. doi: 10.3934/dcds.2010.27.325
[1]

Linping Peng, Zhaosheng Feng, Changjian Liu. Quadratic perturbations of a quadratic reversible Lotka-Volterra system with two centers. Discrete & Continuous Dynamical Systems - A, 2014, 34 (11) : 4807-4826. doi: 10.3934/dcds.2014.34.4807
[2]

Iliya D. Iliev, Chengzhi Li, Jiang Yu. Bifurcations of limit cycles in a reversible quadratic system with a center, a saddle and two nodes. Communications on Pure & Applied Analysis, 2010, 9 (3) : 583-610. doi: 10.3934/cpaa.2010.9.583
[3]

B. Coll, Chengzhi Li, Rafel Prohens. Quadratic perturbations of a class of quadratic reversible systems with two centers. Discrete & Continuous Dynamical Systems - A, 2009, 24 (3) : 699-729. doi: 10.3934/dcds.2009.24.699
[4]

Linping Peng, Yazhi Lei. The cyclicity of the period annulus of a quadratic reversible system with a hemicycle. Discrete & Continuous Dynamical Systems - A, 2011, 30 (3) : 873-890. doi: 10.3934/dcds.2011.30.873
[5]

Yi Shao, Yulin Zhao. The cyclicity of the period annulus of a class of quadratic reversible system. Communications on Pure & Applied Analysis, 2012, 11 (3) : 1269-1283. doi: 10.3934/cpaa.2012.11.1269
[6]

Jaume Llibre, Yilei Tang. Limit cycles of discontinuous piecewise quadratic and cubic polynomial perturbations of a linear center. Discrete & Continuous Dynamical Systems - B, 2019, 24 (4) : 1769-1784. doi: 10.3934/dcdsb.2018236
[7]

Sébastien Gautier, Lubomir Gavrilov, Iliya D. Iliev. Perturbations of quadratic centers of genus one. Discrete & Continuous Dynamical Systems - A, 2009, 25 (2) : 511-535. doi: 10.3934/dcds.2009.25.511
[8]

Ricardo M. Martins, Otávio M. L. Gomide. Limit cycles for quadratic and cubic planar differential equations under polynomial perturbations of small degree. Discrete & Continuous Dynamical Systems - A, 2017, 37 (6) : 3353-3386. doi: 10.3934/dcds.2017142
[9]

Corentin Boissy. Classification of Rauzy classes in the moduli space of Abelian and quadratic differentials. Discrete & Continuous Dynamical Systems - A, 2012, 32 (10) : 3433-3457. doi: 10.3934/dcds.2012.32.3433
[10]

Anton Zorich. Explicit Jenkins-Strebel representatives of all strata of Abelian and quadratic differentials. Journal of Modern Dynamics, 2008, 2 (1) : 139-185. doi: 10.3934/jmd.2008.2.139
[11]

G. Chen, C. Li, C. Liu, Jaume Llibre. The cyclicity of period annuli of some classes of reversible quadratic systems. Discrete & Continuous Dynamical Systems - A, 2006, 16 (1) : 157-177. doi: 10.3934/dcds.2006.16.157
[12]

Yulin Zhao. On the monotonicity of the period function of a quadratic system. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 795-810. doi: 10.3934/dcds.2005.13.795
[13]

Jaume Llibre, Dana Schlomiuk. On the limit cycles bifurcating from an ellipse of a quadratic center. Discrete & Continuous Dynamical Systems - A, 2015, 35 (3) : 1091-1102. doi: 10.3934/dcds.2015.35.1091
[14]

Jaume Llibre, Claudia Valls. Algebraic limit cycles for quadratic polynomial differential systems. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2475-2485. doi: 10.3934/dcdsb.2018070
[15]

José Luis Bravo, Manuel Fernández, Ignacio Ojeda, Fernando Sánchez. Uniqueness of limit cycles for quadratic vector fields. Discrete & Continuous Dynamical Systems - A, 2019, 39 (1) : 483-502. doi: 10.3934/dcds.2019020
[16]

Constantin N. Beli. Representations of integral quadratic forms over dyadic local fields. Electronic Research Announcements, 2006, 12: 100-112.

[17]

Fangfang Jiang, Junping Shi, Qing-guo Wang, Jitao Sun. On the existence and uniqueness of a limit cycle for a Liénard system with a discontinuity line. Communications on Pure & Applied Analysis, 2016, 15 (6) : 2509-2526. doi: 10.3934/cpaa.2016047
[18]

Sze-Bi Hsu, Junping Shi. Relaxation oscillation profile of limit cycle in predator-prey system. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 893-911. doi: 10.3934/dcdsb.2009.11.893
[19]

Amadeu Delshams, Marina Gonchenko, Sergey V. Gonchenko, J. Tomás Lázaro. Mixed dynamics of 2-dimensional reversible maps with a symmetric couple of quadratic homoclinic tangencies. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4483-4507. doi: 10.3934/dcds.2018196
[20]

J. C. Artés, Jaume Llibre, J. C. Medrado. Nonexistence of limit cycles for a class of structurally stable quadratic vector fields. Discrete & Continuous Dynamical Systems - A, 2007, 17 (2) : 259-270. doi: 10.3934/dcds.2007.17.259

2018 Impact Factor: 1.143

Tools

Metrics

  • PDF downloads (21)
  • HTML views (0)
  • Cited by (9)

Other articles
by authors

[Back to Top]

Copyright © 2020 American Institute of Mathematical Sciences