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Volume 9, Number 6, 2019, Pages 2482-2495                                                                DOI:10.11948/20190342
Bifurcation of limit cycles from a compound loop with five saddles
Lijuan Sheng,Maoan Han
Keywords:Limit cycle, bifurcation, Melnikov function, homoclinic loop.
      We concern the number of limit cycles of a polynomial system with degree nine. We prove that under different conditions, the system can have 12 and 20 limit cycles bifurcating from a compound loop with five saddles. Our method relies upon the Melnikov function method and the method of stability-changing of a double homoclinic loop proposed by the authors[J. Yang, Y. Xiong and M. Han, {\em Nonlinear Anal-Theor.}, 2014, 95, 756--773].
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