The Hénon and Lozi attractors are generated by the two discrete-time dynamic systems in the plane, the first one of a quadratic map, and the second of a piecewise smooth map. They are the two systems with the most studied chaotic behavior.

In this paper, our objective is to integrate the two previous maps to obtain a new two-dimensional quadratic piecewise smooth map involving two bifurcation parameters a and b. We show that this map exhibits a chaotic behavior and provides a new chaotic attractor for some values of these two bifurcation parameters a and b.

a new map, quadratic map, two-dimensional, piecewise smooth map.