Dynamics of a 3D autonomous quadratic system with an invariant algebraic surface

An invariant algebraic surface is calculated for a 3D autonomous quadratic system. Also, the dynamics near finite singularities and near infinite singularities on the invariant algebraic surface is analyzed. Furthermore, pitchfork bifurcation is analyzed using center manifold theorem and a first integral of this quadratic system for some special parameters is provided. Finally, the dynamics of this system at infinity using the Poincare compactification in $$R^3$$R3 is investigated and the singularly degenerate heteroclinic cycles are presented by a first integral and verified by numerical simulations.

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