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The center-focus problem and bifurcation of limit cycles in a class of 7th-degree polynomial systems |
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| Authors: | Bo Sang and Qinlong Wang |
| Affiliation: | School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, P. R. China;Guangxi Education Department Key Laboratory of SymbolicComputation and Engineering Data Processing, Hezhou University,Hezhou 542899, Guangxi, P.R. China and Guangxi Education Department Key Laboratory of Symbolic Computation and Engineering Data Processing, Hezhou University,Hezhou 542899, Guangxi, P.R. China;School of Science, Hezhou University, Hezhou 542899, P.R. China |
| Abstract: | By computing singular point values, the center conditions are established for a class of 7th-degree planar polynomial systems with 15 parameters. It is proved that such systems can have 13 small-amplitude limit cycles in the neighborhood of the origin. To the best of our knowledge, this is the first example of a 7th-degree system having non-homogeneous nonlinearities with thirteen limit cycles bifurcated from a fine focus. |
| Keywords: | Limit cycle center variety singular point value time-reversibility. |
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