2 citations · 3 across the 7 of their papers we have counts for
7 papers
A degenerate Takens--Bogdanov bifurcation in a normal form of Lorenz's equations
A. Algaba, M. C. Domínguez-Moreno, M. Merino +1
In this work we consider an unfolding of a normal form of the Lorenz system near a triple-zero singularity. We are interested in the analysis of double-zero bifurcations emerging f…
Centers of quasi-homogeneous polynomial planar systems
A. Algaba, N. Fuentes, C. García
In this paper we determine the centers of quasi-homogeneous polynomial planar vector fields of degree 0, 1, 2, 3 and 4. In addition, in every case we make a study of the reversibil…
Orbital normal forms for a class of three-dimensional systems with an application to Hopf-zero bifurcation analysis of Fitzhugh-Nagumo system
A Algaba, N Fuentes, E Gamero +1
We consider a class of three-dimensional systems having an equilibrium point at the origin, whose principal part is of the form (-Dy h(x, y), Dx h(x,y), f(x,y))^T . This principal…
Non-formally integrable centers admitting an algebraic inverse integrating factor
A. Algaba, N. Fuentes, C. Garcia +1
Westudy the existence of a class of inverse integrating factor for a family of non formally integrable systems, in general, whose lowest-degree quasi-homogeneous term is a Hamilton…
On the Integrability Problem for the Hopf-Zero singularity and its relation with the inverse Jacobi multiplier
A. Algaba, N. Fuentes, E. Gamero +1
In this paper we use the orbital normal form of the nondegenerate Hopf-zero singularity to obtain necessary conditions for the existence of first integrals for such singularity. Al…
The analytic integrability problem for perturbations of homogeneous quadratic Lotka-Volterra systems
Antonio Algaba, Cristóbal García, Manuel Reyes
We solve the analytic integrability problem for diferential systems in the plane whose origin is an isolated singularity and the first homogeneous component is a quadratic Lotka-Vo…