We consider family of quasiperiodically forced dynamical systems given by the map F(θ,x) = (θ + ω mod(1),λf(x + a) ·g(θ)),(2)where θ+ω is an irrational rotation on the unit circle,g(θ)≥ 0 is continuous on the circle.The forced function f:R→R preserves those basic characteristicsof Kellers one in [?],and λ is used as a parameter of this family.