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Hopf bifurcation and centers on center manifold of an extended Bonhoeffer-van der Pol (BVP) oscillator
  • Yusen Wu,
  • Haitao Yue
Yusen Wu
Qufu Normal University

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Haitao Yue
Jining Polytechnic
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In this work, Hopf bifurcation and center problem in a 3-dimensional extended Bonhoeffer-van der Pol (BVP) oscillator with quadratic and cubic nonlinearity are analyzed. Adapting the so-called formal series method for making it able to work with singular point quantities, necessary condition is found for the existence of centers on a local center manifold. Furthermore, Darboux method is employed to prove the sufficiency of the condition. Finally, the exact maximal number of limit cycles that can generate from equilibria via Hopf bifurcation is determined.