Open AccessIntegrability and bifurcation of a three-dimensional circuit differential system
Author(s) -
Brigita Ferčec,
Valery G. Romanovski,
Yilei Tang,
Ling Zhang
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021243
Subject(s) - hopf bifurcation , mathematics , invariant (physics) , lyapunov function , saddle node bifurcation , mathematical analysis , bifurcation , phase space , pitchfork bifurcation , limit (mathematics) , pure mathematics , mathematical physics , physics , nonlinear system , quantum mechanics , thermodynamics
We study integrability and bifurcations of a three-dimensional circuit differential system. The emerging of periodic solutions under Hopf bifurcation and zero-Hopf bifurcation is investigated using the center manifolds and the averaging theory. The zero-Hopf equilibrium is non-isolated and lies on a line filled in with equilibria. A Lyapunov function is found and the global stability of the origin is proven in the case when it is a simple and locally asymptotically stable equilibrium. We also study the integrability of the model and the foliations of the phase space by invariant surfaces. It is shown that in an invariant foliation at most two limit cycles can bifurcate from a weak focus.