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A general formula for the computation of the first Liapunov coefficient corresponding to the Hopf bifurcation in a four‐dimensional system of two coupled identical oscillators is performed for two cases. Only bi‐dimensional vectors are involved. Then a model of two coupled demand–supply systems, depending on four parameters is considered. A study of the Hopf bifurcation is done around one of the symmetrical equilibrium, as the parameters vary. The loci in the parameter space of the parameters values corresponding to subcritical, supercritical or degenerated Hopf bifurcation are found. The computation of the Liapunov coefficients is done using the derived formula. Numerical plots emphasizing the existence of different types of limit cycles are developed. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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de Carvalho Braga Denis Fernando Mello Luis Rocşoreanu Carmen Sterpu Mihaela 《Nonlinear dynamics》2010,62(4):989-1000
Nonlinear Dynamics - On a versal deformation of the Bautin bifurcation it is possible to find dynamical systems that undergo Hopf or non-hyperbolic limit cycle bifurcations. Our paper concerns a... 相似文献
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