On some open problems in planar differential systems and Hilbert’s 16th problem
Author
Abstract
Suggested Citation
DOI: 10.1016/j.chaos.2005.10.057
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
References listed on IDEAS
- Chandrasekar, V.K. & Pandey, S.N. & Senthilvelan, M. & Lakshmanan, M., 2005. "Application of extended Prelle–Singer procedure to the generalized modified Emden type equation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1399-1406.
- Yu, P. & Han, M., 2005. "Small limit cycles bifurcating from fine focus points in cubic order Z2-equivariant vector fields," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 329-348.
- Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
- Wu, Yuhai & Han, Maoan & Liu, Xuanliang, 2005. "On the study of limit cycles of a cubic polynomials system under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 24(4), pages 999-1012.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
Cited by:
- Liu, Yuanyuan & He, Dongping & Huang, Wentao, 2023. "Weak centers and local criticality on planar Z2-symmetric cubic differential systems," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
Most related items
These are the items that most often cite the same works as this one and are cited by the same works as this one.- Singh, Vimal, 2008. "Novel frequency-domain criterion for elimination of limit cycles in a class of digital filters with single saturation nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 38(1), pages 178-183.
- Singh, Vimal, 2007. "A new frequency-domain criterion for elimination of limit cycles in fixed-point state-space digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 813-816.
- Singh, Vimal, 2008. "Suppression of limit cycles in second-order companion form digital filters with saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 677-681.
- Wang, S. & Yu, P., 2006. "Existence of 121 limit cycles in a perturbed planar polynomial Hamiltonian vector field of degree 11," Chaos, Solitons & Fractals, Elsevier, vol. 30(3), pages 606-621.
- Yu, P. & Han, M., 2007. "On limit cycles of the Liénard equation with Z2 symmetry," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 617-630.
- Singh, Vimal, 2007. "Modified LMI condition for the realization of limit cycle-free digital filters using saturation arithmetic," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1448-1453.
- Wu, Yuhai & Tian, Lixin & Hu, Yingjing, 2007. "On the limit cycles of a Hamiltonian under Z4-equivariant quintic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 298-307.
- Ting Huang & Jieping Gu & Yuting Ouyang & Wentao Huang, 2023. "Bifurcation of Limit Cycles and Center in 3D Cubic Systems with Z 3 -Equivariant Symmetry," Mathematics, MDPI, vol. 11(11), pages 1-22, June.
- Yu, P. & Han, M., 2006. "Limit cycles in generalized Liénard systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1048-1068.
- Tsai, Hsun-Heng & Fuh, Chyun-Chau, 2007. "Combining dither smoothing technique and state feedback linearization to control undifferentiable chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 886-895.
- Wang, S. & Yu, P., 2005. "Bifurcation of limit cycles in a quintic Hamiltonian system under a sixth-order perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1317-1335.
- Cui, Yan & Liu, Suhua & Tang, Jiashi & Meng, Yimin, 2009. "Amplitude control of limit cycles in Langford system," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 335-340.
- Yang, Junmin & Yu, Pei, 2017. "Nine limit cycles around a singular point by perturbing a cubic Hamiltonian system with a nilpotent center," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 141-152.
- Han, Maoan & Zang, Hong & Zhang, Tonghua, 2007. "A new proof to Bautin’s theorem," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 218-223.
- Han, Maoan & Xiong, Yanqin, 2014. "Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters," Chaos, Solitons & Fractals, Elsevier, vol. 68(C), pages 20-29.
- Ye, Zhiyong & Han, Maoan, 2006. "Singular limit cycle bifurcations to closed orbits and invariant tori," Chaos, Solitons & Fractals, Elsevier, vol. 27(3), pages 758-767.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:31:y:2007:i:5:p:1118-1134. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .
Please note that corrections may take a couple of weeks to filter through the various RePEc services.