In 1978, Lozi introduced a new chaotic map in two dimensions wherein equations and attractors resemble with those of the famous maps of Hénon. Simply, a quadratic term in it is replaced by another piecewise linear term in the first equation. In this paper, we study the Lozi map by replacing the piecewise linear term in the first equation by the function   This is a family model that allows us to study several new piecewise-smooth maps. We demonstrate that these models converge to a robust chaotic attractor and give some applications of these models in the real world.

a new family of Lozi maps, max function.