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DERIVATION OF ISOCHRONICITY CONDITIONS FOR QUASI-CUBIC HOMOGENEOUS ANALYTIC SYSTEMS
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| Organization: | School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang |
| Organization: | School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang |
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| International Journal of Bifurcation and Chaos |
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In this article, we deal with the problems of characterizing isochronous centers for real planar quasi-cubic homogeneous analytic system. The technique is based on reducing the quasi-cubic analytic system into an analytic system. With the help of common computer algebra software- MATHEMATICA, we compute the period constants of the origin and obtain the necessary isochronous center conditions for the transformed system. Finally, we give a proof of the sufficiency by various methods. Similar results are less so far. Our work is new in terms of research about quasi-cubic analytic system and consists of the existing results related to cubic polynomial system as a special case. What is worth pointing out is that we offer a kind of interesting phenomenon that the exponent parameter λ controls the nonanalyticity of the studied system (5).
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Period constant, isochronous center, quasi-cubic analytic system
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