  Chaos transition, as an important topic, has become an active research
subject in non-linear science. By considering a Dicke Hamiltonian coupled to a
bath of harmonic oscillator, we have been able to introduce a logistic map with
quantum corrections. Some basic dynamical properties, such as Lyapunov
exponents and bifurcation diagram of the model are studied. we show that in
this model, the transition from integrable motion to periodic, chaotic and
hyperchaotic as the control parameter $r$ is increased.
