The neural firing activities related to information coding maintaining the information
transmission vary qualitatively considering the electromagnetic induction. The firing of a …

The usual averaging theory reduces the computation of some periodic solutions of a system
of ordinary differential equations, to find the simple zeros of an associated averaged …

We study the Hopf and the fold–Hopf bifurcations of the Rössler–type differential system x=−
y− z, y= x+ ay, z=− cz+ byz, with b= 0. We show that the classical Hopf bifurcation cannot be …

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. Also, we …

The FitzHugh-Nagumo system is a $4 $-parameter family of $3 $ D vector field used for
modeling neural excitation and nerve impulse propagation. The origin represents a Hopf …

We consider a class of three-dimensional systems having an equilibrium point at the origin,
whose principal part is of the form (−∂ h∂ y (x, y),∂ h∂ x (x, y), f (x, y)) T. This principal …

This paper is devoted to study the zero-Hopf bifurcation of the three dimensional Lotka-
Volterra systems. The explicit conditions for the existence of two first integrals for the system …

We investigate a periodic solution which bifurcates from a curve of the singularity of the jerk
system in. More precisely, we give the explicit states for the existence of a periodic solution …

By computing we obtain that P1 (0, 0, 1) is a zero-Hopf equilibrium point of nuclear spin
generator system. We prove that there exist two families of nuclear spin generator system …

This work presents new results in the averaging theory for finding periodic solutions. Using
Lyapunov-Schmidt reduction and Brouwer's degree we elaborate an averaging theorem …