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The Hopf Bifurcations in the Permanent Magnet Synchronous Motors
  
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KeyWord:Focus quantity; Limit cycle; Hopf bifurcation
Author NameAffiliation
Bo Sang School of Mathematical Sciences, Liaocheng University, Liaocheng, Shandong 252059, China 
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Abstract:
      Based on the focus quantities and other techniques, the stability properties of equilibria and the limit cycles arising from Hopf bifurcations are investigated for two models of permanent magnet synchronous motors. The first model is of surface-magnet type and can have at most two unstable small limit cycles, which are symmetric with respect to $x$-axis. The other model is of interior-magnet type and can have at most four small limit cycles in two symmetric nests.