We give the normal forms of all polynomial differential systems in R-3 which have a nondegenerate or degenerate quadric as an invariant algebraic surface. We also characterize among these systems those which have a Darboux ...

We characterize all the planar polynomial differential systems with a unique invariant algebraic curve given by a real conic and having a Darboux invariant.

In this paper, we present the global phase portraits in the Poincaré disc of the planar quadratic polynomial systems which admit invariant straight lines with total multiplicity two and Darboux invariants.

In this paper, we give an algebraic criterion to determine the nonchaotic behavior for polynomial differential systems defined in ℝ3 and, using this result, we give a partial positive answer for the conjecture about the ...

Invariant algebraic surfaces are commonly observed in differential systems arising in mathematical modeling of natural phenomena. In this paper, we study the integrability and dynamics of quadratic polynomial differential ...