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Multiple limit cycles bifurcation and Jacobi stability for a class of segmented disc dynamo system
  • Hongpu Liu,
  • Qinlong Wang,
  • Wentao Huang
Hongpu Liu
Sun Yat-sen University - Zhuhai Campus
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Qinlong Wang
Guilin University of Electronic Technology

Corresponding Author:[email protected]

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Wentao Huang
Guilin University of Electronic Technology
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In this paper, the multiple bifurcation of limit cycles for a segmented disc dynamo system is studied. The formal series method for calculating the singular point quantities is applied to determine the highest order focus value at Hopf bifurcation point. For two cases of the segmented disc dynamo system, namely the system with or without friction coefficient (abbr. SDDF- or SDD-model), the maximum number of limit cycles is obtained at the symmetrical equilibrium points under the condition of synchronous perturbation respectively. At the same time, the parameters condition is classified for exact number of limit cycles near each weak focus. Finally, we find that all equilibrium points of the heart model are Jacobi unstable under certain parameter values.