Liu, Yirong; Huang, Wentao Seven large-amplitude limit cycles in a cubic polynomial system. (English) Zbl 1111.37035 Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 2, 473-485 (2006). Summary: The problem of limit cycles bifurcated from the equator for a cubic polynomial system is investigated. The best result so far in the literature for this problem is six limit cycles. By using the method of singular point value, we prove that a cubic polynomial system can bifurcate seven limit cycles from the equator. We also find that a rational system has an isochronous center at the equator. Cited in 10 Documents MSC: 37G15 Bifurcations of limit cycles and periodic orbits in dynamical systems 34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations 34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations 37C10 Dynamics induced by flows and semiflows Keywords:focal value; singular point value; infinity; limit cycle; isochronous center PDFBibTeX XMLCite \textit{Y. Liu} and \textit{W. Huang}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 16, No. 2, 473--485 (2006; Zbl 1111.37035) Full Text: DOI References: [1] Bautin N. N., Amer. Math. Soc. Trans. 100 pp 397– [2] DOI: 10.1006/jdeq.1993.1070 · Zbl 0778.34024 [3] Cheng H. B., Chinese Ann. Math. A 24 pp 219– [4] Gobber F., J. Math. Anal. Appl. 71 pp 330– [5] DOI: 10.1016/j.bulsci.2004.02.002 · Zbl 1070.34064 [6] James E. M., I.M.A.J. Applied Math. 47 pp 163– [7] Liu Y. R., Science in China (Series A) 44 pp 37– [8] DOI: 10.1016/S0898-1221(02)00209-2 · Zbl 1084.34523 [9] Liu Y. R., Acta Math. Appl. Sin. 25 pp 295– [10] DOI: 10.1016/S0007-4497(02)00006-4 · Zbl 1034.34032 [11] Liu Y. R., Science in China (Series A) 33 pp 10– [12] DOI: 10.1016/0893-9659(94)90005-1 · Zbl 0804.34033 [13] DOI: 10.1088/0951-7715/8/5/011 · Zbl 0837.34042 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.