Abstract
In this paper, we study the appearance of limit cycles from the equator and pseudo-isochronicity at infinity in a class of septic polynomial vector field with no singular point at infinity. We solve the problems by an indirect method, i.e., we transform infinity into the origin so that we can investigate the properties of infinity with the methods developed for finite critical point. Further, we construct a septic system which has six limit cycles in the neighborhood of infinity. Finally, we investigate the pseudo-isochronous center conditions at infinity for the system. As far as we know, this is the first time that the bifurcation of limit cycles and pseudo-isochronous center conditions at infinity in a septic system are simultaneously discussed.
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This work is supported in part by the National Nature Science Foundation of China (NSFC 11101126 and 11101127) and Scientific Research Foundation for Doctoral Scholars of HAUST (09001524).
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Wu, Y., Liu, L. Bifurcation of Limit Cycles and Pseudo-Isochronicity at Infinity in a Septic Polynomial Vector Field. Qual. Theory Dyn. Syst. 11, 417–433 (2012). https://doi.org/10.1007/s12346-011-0064-7
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DOI: https://doi.org/10.1007/s12346-011-0064-7