24 citations · 49 across the 8 of their papers we have counts for
11 papers
Nilpotent Feed Forward Network Dynamics
Fahimeh Mokhtari
In this paper, we explore the normal form of fully inhomogeneous feed forward network dynamical systems, characterized by a nilpotent linear component. We introduce a new normal fo…
Bifurcations of Riemann Ellipsoids
Fahimeh Mokhtari, Jesús F. Palacián, Patricia Yanguas
We give an account of the various changes in the stability character in the five types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian…
The Lie algebraic structure of colored networks
Fahimeh Mokhtari, Jan Sanders
In the computation of the normal form of a colored network vector field, following the semigroup(oid) approach in [19], one would like to be able to say something about the structu…
Normal form for maps with nilpotent linear part
Fahimeh Mokhtari, Ernst Roell, Jan Sanders
The normal form for an n-dimensional map with irreducible nilpotent linear part is determined using sl2-representation theory. We sketch by example how the reducible case can also…
Equivariant decomposition of polynomial vector fields
Fahimeh Mokhtari, Jan A. Sanders
To compute the unique formal normal form of families of vector fields with nilpotent linear part, we choose a basis of the Lie algebra consisting of orbits under the linear nilpote…
On the representations and -equivariant normal form for solenoidal Hopf-zero singularities
Fahimeh Mokhtari
In this paper, we deal with the solenoidal conservative Lie algebra associated to the classical normal form of Hopf-zero singular system. We concentrate on the study of some repres…
Versal Normal Form for Nonsemisimple Singularities
Fahimeh Mokhtari, Jan. A Sanders
The theory of versal normal form has been playing a role in normal form since the introduction of the concept by V.I. Arnol'd. But there has been no systematic use of it that is in…
Vector potential normal form classification for completely integrable solenoidal nilpotent singularities
Majid Gazor, Fahimeh Mokhtari, Jan A. Sanders
We introduce a sl_2-invariant family of nonlinear vector fields with a non-semisimple triple zero singularity. In this paper we are concerned with characterization and normal form…
Normal Forms of Hopf-zero singularity
Majid Gazor, Fahimeh Mokhtari
The Lie algebra generated by Hopf-zero classical normal forms is decomposed into two versal Lie subalgebras. Some dynamical properties for each subalgebra are described; one is the…
Volume-preserving normal forms of Hopf-zero singularity
Majid Gazor, Fahimeh Mokhtari
A practical method is described for computing the unique generator of the algebra of first integrals associated with a large class of Hopf-zero singularity. The set of all volume-p…
Normal forms for Hopf-Zero singularities with nonconservative nonlinear part
Majid Gazor, Fahimeh Mokhtari, Jan A. Sanders
In this paper we are concerned with the simplest normal form computation of a family of Hopf-zero vector fields without a first integral. This family of vector fields are the class…