Susanna Maza

On the periodic orbit bifurcating from a zero Hopf bifurcation in systems with two slow and one fast variables

The Hopf bifurcation in slow-fast systems with two slow variables and one fast variable has been studied recently, mainly from a numerical point of view. Our goal is to provide an analytic proof of the existence of the zero Hopf bifurcation exhibited for such systems, and to characterize the stability or instability of the periodic orbit which borns in such zero Hopf bifurcation. Our proofs use the averaging theory.

ORBITAL LINEARIZATION IN THE QUADRATIC LOTKA–VOLTERRA SYSTEMS AROUND SINGULAR POINTS VIA LIE SYMMETRIES

In this paper, we consider linearizability and orbital linearizability properties of the Lotka–Volterra system in the neighborhood of a singular point with eigenvalues 1 and -q. In this paper we give the explicit smooth near-identity change of variables that linearizes or orbital linearizes such Lotka–Volterra system with q ∈ ℕ\{0, 1} being seen that these changes are also valid for q ∈ ℂ\{0, 1}.

Inverse Jacobi Multipliers: Recent Applications in Dynamical Systems

In this paper we show novel applications of the inverse Jacobi multiplier focusing on questions of bifurcations and existence of periodic solutions admitted by both autonomous and non-autonomous systems of ordinary differential equations. In the autonomous case we focus on dimension n ≥ 3 whereas in the non-autonomous we study the cases with n ≥ 2. We summarize results already published and additionally we state some recent results to appear. The principal object of this research is two fold: first to prove the existence and smoothness of inverse Jacobi multiplier V in the region of interest in the phase space and second to show that the invariant set under the flow given by the zero-set of an inverse Jacobi multiplier contains under some assumptions orbits which are relevant in its phase portrait such as periodic orbits, limit cycles, stable, unstable and center manifolds and so on. In the non-autonomous T-periodic case we show some relationships between T-periodic orbits and T-periodic inverse Jacobi multipliers.

Linearization of non-degenerate analytic centres in

In this paper, we study the linearization problem of a non-degenerate analytic centre on a centre manifold in . We show how the case of constant divergence of the associated vector field can be linearized with the help of inverse Jacobi multipliers. Moreover, we also combine methods of Lie symmetries from a given analytic commutator with linear part without resonances to get explicitly the linearizing change of variables. Finally, we show how the methods work in some examples.

Centers in a Quadratic System Obtained from a Scalar Third Order Differential Equation

In this paper it is shown that (0,0,0) is a center for

The reversibility and the center problem

\displaystyle{\dot{x} = y,\quad \dot{y} = z,\quad \dot{z} = -\frac{1} {a}\,z - a\,(2x + 1)y - x(x + 1)}

A new approach to center conditions for simple analytic monodromic singularities

and that (−1,0,0) is a center for