  We focus on a chaotic differential system in 3-dimension, including an
absolute term and a line of equilibrium points. Which describes in the
following This system has an implementation in electronic components. The first
purpose of this paper is to provide sufficient conditions for the existence of
a limit cycle bifurcating from the zeroHopf equilibrium point located at the
origin of the coordinates. The second aim is to study the integrability of each
differential system, one defined in half-space y and the other in half-space y.
We prove that these two systems have no polynomial, rational, or Darboux first
integrals for any value of a, b, and c. Furthermore, we provide a formal series
and an analytic first integral of these systems. We also classify Darboux
polynomials and exponential factors.
