Continuum of limit cycles in a class of three-dimensional quadratic polynomial systems

It is well-known that planar autonomous polynomial dynamical systems have only a finite number of limit cycles. We present a class of parameter depending three-dimensional autonomous systems whose right-hand side consists of quadratic polynomials and establish the bifurcation of a continuum of limit cycles from a period annulus and from an equilibrium point. A limit cycle Γ is understood as a closed orbit without equilibrium point which is the limit set of a trajectory different from Γ . The systems under consideration are distinguished by the existence of two straight lines of equilibria and the existence of a family of invariant manifolds foliating R 3 ∖ { 0 } .