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Hopf bifurcation and the centers on center manifold for a class of three‐dimensional Circuit system
Author(s) -
Huang Wentao,
Wang Qinlong,
Chen Aiyong
Publication year - 2019
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6026
Subject(s) - center manifold , mathematics , hopf bifurcation , singular point of a curve , center (category theory) , bifurcation , manifold (fluid mechanics) , bifurcation theory , limit (mathematics) , pitchfork bifurcation , saddle node bifurcation , transcritical bifurcation , mathematical analysis , nonlinear system , mechanical engineering , chemistry , physics , quantum mechanics , engineering , crystallography
In this paper, Hopf bifurcation and center problem for a generic three‐dimensional Chua's circuit system are studied. Applying the formal series method of computing singular point quantities to investigate the two cases of the generic circuit system, we find necessary conditions for the existence of centers on a local center manifold for the systems, then Darboux method is applied to show the sufficiency. Further, we determine the maximum number of limit cycles that can bifurcate from the corresponding equilibrium via Hopf bifurcation.