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| Hopf Bifurcation and Centers on Center Manifold of an Extended Bonhoeffer-Van der Pol (BVP) Oscillator |
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| KeyWord:Hopf bifurcation, centers on center manifold, extended Bonhoeffer-van der Pol (BVP) oscillator, singular point quantity |
| Author Name | Affiliation | | Yangtao Li | School of Mathematics and Statistics, Henan University of Science and Technology, No. 263 Kaiyuan Road, 271023 Luoyang, P. R. China | | Wenyi Wang | School of Mathematics and Statistics, Henan University of Science and Technology, No. 263 Kaiyuan Road, 271023 Luoyang, P. R. China | | Yusen Wu | School of Mathematics and Statistics, Henan University of Science and Technology, No. 263 Kaiyuan Road, 271023 Luoyang, P. R. China |
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| Abstract: |
| 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 to work with singular point quantities, a necessary condition is found for the existence of centers on a local center manifold. Furthermore, the Darboux method is employed to prove the sufficiency of the condition. Finally, the exact maximal number of limit cycles that can be generated from equilibria via Hopf bifurcation is determined. |
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