Xiong, Yanqin On the number of limit cycles near a homoclinic loop with a nilpotent cusp of order \(m\). (English) Zbl 07791836 J. Differ. Equations 380, 146-180 (2024). Reviewer: Maite Grau (Lleida) MSC: 34C05 34C23 34C37 PDFBibTeX XMLCite \textit{Y. Xiong}, J. Differ. Equations 380, 146--180 (2024; Zbl 07791836) Full Text: DOI
Xiong, Yanqin; Hu, Jianqiang Double homoclinic bifurcations by perturbing a class of cubic \(\mathrm{Z}_2\)-equivariant polynomial systems with nilpotent singular points. (English) Zbl 07786260 Bull. Sci. Math. 190, Article ID 103377, 21 p. (2024). MSC: 37J20 37G20 37G40 37C29 PDFBibTeX XMLCite \textit{Y. Xiong} and \textit{J. Hu}, Bull. Sci. Math. 190, Article ID 103377, 21 p. (2024; Zbl 07786260) Full Text: DOI
Chen, Hebai; Chen, Xingwu; Jia, Man; Tang, Yilei A quintic \(\mathbb{Z}_2\)-equivariant Liénard system arising from the complex Ginzburg-Landau equation. (English) Zbl 07763741 SIAM J. Math. Anal. 55, No. 6, 5993-6038 (2023). Reviewer: Qinlong Wang (Guilin) MSC: 34C05 34C14 34C20 34C23 34C37 PDFBibTeX XMLCite \textit{H. Chen} et al., SIAM J. Math. Anal. 55, No. 6, 5993--6038 (2023; Zbl 07763741) Full Text: DOI
Zhang, Xiaolei; Xiong, Yanqin; Zhang, Yi The number of limit cycles by perturbing a piecewise linear system with three zones. (English) Zbl 1501.34021 Commun. Pure Appl. Anal. 21, No. 5, 1833-1855 (2022). Reviewer: Zhengdong Du (Chengdu) MSC: 34A36 34C05 34C07 34E10 34C23 37J40 34A30 PDFBibTeX XMLCite \textit{X. Zhang} et al., Commun. Pure Appl. Anal. 21, No. 5, 1833--1855 (2022; Zbl 1501.34021) Full Text: DOI
Xiong, Yanqin; Wang, Cheng Limit cycle bifurcations of planar piecewise differential systems with three zones. (English) Zbl 1478.34042 Nonlinear Anal., Real World Appl. 61, Article ID 103333, 18 p. (2021). MSC: 34C07 34C23 34C05 PDFBibTeX XMLCite \textit{Y. Xiong} and \textit{C. Wang}, Nonlinear Anal., Real World Appl. 61, Article ID 103333, 18 p. (2021; Zbl 1478.34042) Full Text: DOI
Chen, Jiayi; Tian, Yun Maximum number of small limit cycles in some rational Liénard systems with cubic restoring terms. (English) Zbl 1490.34035 Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 12, Article ID 2150176, 9 p. (2021). Reviewer: Alexander Grin (Grodno) MSC: 34C07 34C05 34C23 34B30 PDFBibTeX XMLCite \textit{J. Chen} and \textit{Y. Tian}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 31, No. 12, Article ID 2150176, 9 p. (2021; Zbl 1490.34035) Full Text: DOI
Xiong, Yanqin; Han, Maoan Limit cycles appearing from a generalized heteroclinic loop with a cusp and a nilpotent saddle. (English) Zbl 1489.34051 J. Differ. Equations 303, 575-607 (2021). Reviewer: Iliya Iliev (Sofia) MSC: 34C07 34C05 34C23 34C37 34A36 34E10 PDFBibTeX XMLCite \textit{Y. Xiong} and \textit{M. Han}, J. Differ. Equations 303, 575--607 (2021; Zbl 1489.34051) Full Text: DOI
Yang, Junmin; Yu, Pei; Han, Maoan On the Melnikov functions and limit cycles near a double homoclinic loop with a nilpotent saddle of order \(\hat{m} \). (English) Zbl 1471.37055 J. Differ. Equations 291, 27-56 (2021). MSC: 37J20 37G15 37C29 PDFBibTeX XMLCite \textit{J. Yang} et al., J. Differ. Equations 291, 27--56 (2021; Zbl 1471.37055) Full Text: DOI
Cai, Junning; Wei, Minzhi; Zhu, Hongying Nine limit cycles in a 5-degree polynomials Liénard system. (English) Zbl 1454.34065 Complexity 2020, Article ID 8584616, 10 p. (2020). MSC: 34C23 34C37 PDFBibTeX XMLCite \textit{J. Cai} et al., Complexity 2020, Article ID 8584616, 10 p. (2020; Zbl 1454.34065) Full Text: DOI
Xiong, Yanqin; Cheng, Rong; Li, Na Limit cycle bifurcations in perturbations of a reversible quadratic system with a non-rational first integral. (English) Zbl 1461.34063 Qual. Theory Dyn. Syst. 19, No. 3, Paper No. 97, 28 p. (2020). Reviewer: Jihua Yang (Guyuan) MSC: 34C23 34C05 34E10 34C07 34A36 34A05 PDFBibTeX XMLCite \textit{Y. Xiong} et al., Qual. Theory Dyn. Syst. 19, No. 3, Paper No. 97, 28 p. (2020; Zbl 1461.34063) Full Text: DOI
Xiong, Yanqin; Han, Maoan Limit cycle bifurcations by perturbing a class of planar quintic vector fields. (English) Zbl 1454.34057 J. Differ. Equations 269, No. 12, 10964-10994 (2020). Reviewer: Jeidy Johana Jimenez (Goiânia) MSC: 34C05 34C07 34C23 34C08 PDFBibTeX XMLCite \textit{Y. Xiong} and \textit{M. Han}, J. Differ. Equations 269, No. 12, 10964--10994 (2020; Zbl 1454.34057) Full Text: DOI
Álvarez, M. J.; Coll, B.; De Maesschalck, P.; Prohens, R. Asymptotic lower bounds on Hilbert numbers using canard cycles. (English) Zbl 1460.34039 J. Differ. Equations 268, No. 7, 3370-3391 (2020). Reviewer: Klaus R. Schneider (Berlin) MSC: 34C07 34C05 34E15 34E17 PDFBibTeX XMLCite \textit{M. J. Álvarez} et al., J. Differ. Equations 268, No. 7, 3370--3391 (2020; Zbl 1460.34039) Full Text: DOI
Li, Linlin; Yang, Junmin On the number of limit cycles for a quintic Liénard system under polynomial perturbations. (English) Zbl 1457.34052 J. Appl. Anal. Comput. 9, No. 6, 2464-2481 (2019). MSC: 34C07 PDFBibTeX XMLCite \textit{L. Li} and \textit{J. Yang}, J. Appl. Anal. Comput. 9, No. 6, 2464--2481 (2019; Zbl 1457.34052) Full Text: DOI
Xiong, Yanqin; Hu, Jianqiang A class of reversible quadratic systems with piecewise polynomial perturbations. (English) Zbl 1433.34049 Appl. Math. Comput. 362, Article ID 124527, 17 p. (2019). MSC: 34C07 34C05 34C23 37G15 PDFBibTeX XMLCite \textit{Y. Xiong} and \textit{J. Hu}, Appl. Math. Comput. 362, Article ID 124527, 17 p. (2019; Zbl 1433.34049) Full Text: DOI
Li, Shimin; Llibre, Jaume Phase portraits of piecewise linear continuous differential systems with two zones separated by a straight line. (English) Zbl 1412.34111 J. Differ. Equations 266, No. 12, 8094-8109 (2019). Reviewer: Marco Spadini (Firenze) MSC: 34C05 34C37 34C07 37G15 PDFBibTeX XMLCite \textit{S. Li} and \textit{J. Llibre}, J. Differ. Equations 266, No. 12, 8094--8109 (2019; Zbl 1412.34111) Full Text: DOI Link
Yang, Junmin; Ding, Wei Limit cycles of a class of Liénard systems with restoring forces of seventh degree. (English) Zbl 1426.34041 Appl. Math. Comput. 316, 422-437 (2018). MSC: 34C05 34C07 34C23 PDFBibTeX XMLCite \textit{J. Yang} and \textit{W. Ding}, Appl. Math. Comput. 316, 422--437 (2018; Zbl 1426.34041) Full Text: DOI
Xiong, Yanqin; Hu, Jianqiang; Li, Shimin; Li, Jingzheng Center problem for quasi-homogeneous polynomial systems with a given weight degrees. (English) Zbl 1412.34115 Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 14, Article ID 1850174, 10 p. (2018). MSC: 34C05 34C25 PDFBibTeX XMLCite \textit{Y. Xiong} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 14, Article ID 1850174, 10 p. (2018; Zbl 1412.34115) Full Text: DOI
Zhu, Hongying; Qin, Bin; Yang, Sumin; Wei, Minzhi Poincaré bifurcation of some nonlinear oscillator of generalized Liénard type using symbolic computation methods. (English) Zbl 1397.34071 Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 8, Article ID 1850096, 13 p. (2018). MSC: 34C23 34C15 34E10 34C05 34C37 34-04 PDFBibTeX XMLCite \textit{H. Zhu} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 28, No. 8, Article ID 1850096, 13 p. (2018; Zbl 1397.34071) Full Text: DOI
Xiong, Yanqin Limit cycle bifurcations by perturbing non-smooth Hamiltonian systems with 4 switching lines via multiple parameters. (English) Zbl 1388.34013 Nonlinear Anal., Real World Appl. 41, 384-400 (2018). Reviewer: Stathis Antoniou (Athína) MSC: 34A36 34C05 34C23 34E10 34C07 PDFBibTeX XMLCite \textit{Y. Xiong}, Nonlinear Anal., Real World Appl. 41, 384--400 (2018; Zbl 1388.34013) Full Text: DOI
Han, Maoan; Sheng, Lijuan; Zhang, Xiang Bifurcation theory for finitely smooth planar autonomous differential systems. (English) Zbl 1410.34116 J. Differ. Equations 264, No. 5, 3596-3618 (2018). Reviewer: Alois Steindl (Wien) MSC: 34C23 34C07 34C05 34E10 PDFBibTeX XMLCite \textit{M. Han} et al., J. Differ. Equations 264, No. 5, 3596--3618 (2018; Zbl 1410.34116) Full Text: DOI
Hu, Huan; Shen, Jianhe; Zhou, Zheyan; Ou, Zhonghui Relaxation oscillations in singularly perturbed generalized Liénard systems with non-generic turning points. (English) Zbl 1488.34254 Math. Model. Anal. 22, No. 3, 389-407 (2017). MSC: 34C26 34E17 34E20 34E15 34E05 34C20 92D25 34C23 PDFBibTeX XMLCite \textit{H. Hu} et al., Math. Model. Anal. 22, No. 3, 389--407 (2017; Zbl 1488.34254) Full Text: DOI
Sun, Xianbo Perturbation of a period annulus bounded by a heteroclinic loop connecting two hyperbolic saddles. (English) Zbl 1385.37077 Qual. Theory Dyn. Syst. 16, No. 1, 187-203 (2017). Reviewer: Vladimir Răsvan (Craiova) MSC: 37J40 37J45 37J25 34C07 PDFBibTeX XMLCite \textit{X. Sun}, Qual. Theory Dyn. Syst. 16, No. 1, 187--203 (2017; Zbl 1385.37077) Full Text: DOI
Li, Shimin; Cen, Xiuli; Zhao, Yulin Bifurcation of limit cycles by perturbing piecewise smooth integrable non-Hamiltonian systems. (English) Zbl 1354.34070 Nonlinear Anal., Real World Appl. 34, 140-148 (2017). Reviewer: Iliya Iliev (Sofia) MSC: 34C23 34A36 34C05 PDFBibTeX XMLCite \textit{S. Li} et al., Nonlinear Anal., Real World Appl. 34, 140--148 (2017; Zbl 1354.34070) Full Text: DOI
Wu, Kuilin; Li, Shimin Limit cycles for perturbing Hamiltonian system inside piecewise smooth polynomial differential system. (English) Zbl 1419.34066 Adv. Difference Equ. 2016, Paper No. 228, 8 p. (2016). MSC: 34A36 34C07 37J45 PDFBibTeX XMLCite \textit{K. Wu} and \textit{S. Li}, Adv. Difference Equ. 2016, Paper No. 228, 8 p. (2016; Zbl 1419.34066) Full Text: DOI
Li, Shimin; Wu, Kuilin On the limit cycles bifurcating from piecewise quasi-homogeneous differential center. (English) Zbl 1343.34043 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 7, Article ID 1650116, 10 p. (2016). MSC: 34A36 34C23 34C05 PDFBibTeX XMLCite \textit{S. Li} and \textit{K. Wu}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 7, Article ID 1650116, 10 p. (2016; Zbl 1343.34043) Full Text: DOI
Asheghi, R.; Bakhshalizadeh, A. On the distribution of limit cycles in a Liénard system with a nilpotent center and a nilpotent saddle. (English) Zbl 1334.34073 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 2, Article ID 1650025, 15 p. (2016). MSC: 34C07 34C08 34C05 PDFBibTeX XMLCite \textit{R. Asheghi} and \textit{A. Bakhshalizadeh}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 2, Article ID 1650025, 15 p. (2016; Zbl 1334.34073) Full Text: DOI
Sheng, Lijuan Limit cycles of a class of piecewise smooth Liénard systems. (English) Zbl 1334.34079 Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 1, Article ID 1650009, 10 p. (2016). MSC: 34C07 34C23 34C05 34A36 PDFBibTeX XMLCite \textit{L. Sheng}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 26, No. 1, Article ID 1650009, 10 p. (2016; Zbl 1334.34079) Full Text: DOI arXiv
Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín; Sadovskaia, Natalia The 16th Hilbert problem restricted to circular algebraic limit cycles. (English) Zbl 1346.34028 J. Differ. Equations 260, No. 7, 5726-5760 (2016). Reviewer: Alexander Grin (Grodno) MSC: 34C07 34A05 PDFBibTeX XMLCite \textit{J. Llibre} et al., J. Differ. Equations 260, No. 7, 5726--5760 (2016; Zbl 1346.34028) Full Text: DOI
Sun, Xianbo Multiple limit cycles of some strongly nonlinear Liénard-van der Pol oscillator. (English) Zbl 1410.34098 Appl. Math. Comput. 270, 620-630 (2015). MSC: 34C07 34C37 37G15 34C05 PDFBibTeX XMLCite \textit{X. Sun}, Appl. Math. Comput. 270, 620--630 (2015; Zbl 1410.34098) Full Text: DOI
Liang, Haihua; Torregrosa, Joan Parallelization of the Lyapunov constants and cyclicity for centers of planar polynomial vector fields. (English) Zbl 1334.34070 J. Differ. Equations 259, No. 11, 6494-6509 (2015). Reviewer: A. P. Sadovskii (Minsk) MSC: 34C05 34C25 34C07 PDFBibTeX XMLCite \textit{H. Liang} and \textit{J. Torregrosa}, J. Differ. Equations 259, No. 11, 6494--6509 (2015; Zbl 1334.34070) Full Text: DOI
Han, Maoan; Xiong, Yanqin Limit cycle bifurcations in a class of near-Hamiltonian systems with multiple parameters. (English) Zbl 1354.34062 Chaos Solitons Fractals 68, 20-29 (2014). MSC: 34C07 37J40 37J20 PDFBibTeX XMLCite \textit{M. Han} and \textit{Y. Xiong}, Chaos Solitons Fractals 68, 20--29 (2014; Zbl 1354.34062) Full Text: DOI