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 ...

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 ...

In this paper we give the normal form of all polynomial differential systems in R3 having a weighted homogeneous surface f= 0 as an invariant algebraic surface and characterize among these systems those having a Darboux ...

In this paper by using the Poincare compactification of R(3) we describe the global dynamics of the Lorenz system(x) over dot = s(-x + y), (y) over dot = rx - y - xz, (z) over dot = -bz + xy,having some invariant algebraic ...

We investigate the classification of closed curves and eight curves of saddle points defined on non-orientable closed surfaces, up to an ambient homeomorphism. The classification obtained here is applied to Morse–Bott ...

We consider the well-known Sprott A system, which depends on a single real parameter a and, for a= 1 , was shown to present a hidden chaotic attractor. We study the formation of hidden chaotic attractors as well as the ...

We present a global dynamical analysis of the following quadratic differential system (Formula presented.) , where (Formula presented.) are the state variables and a, b, d, f, g are real parameters. This system has been ...

Polynomial vector fields X: R3→ R3 that have invariant algebraic surfaces of the form M={f(x,y)z-g(x,y)=0}are considered. We prove that trajectories of X on M are solutions of a constrained differential system having I= { ...