Soft Transition between Type-I and -III Intermittencies in a Nonlinear Map

9),lQ) showed up a new phenomenon, that is a continuous transition between type-I and -III intermittencies. To explain some of the features of this transition, we proposed a seventh degree polynomial map,IO) which had a similar shape to the actual return maps found in the oscillator problem. To simplify the model with respect to the oscillator case, we proposed a map with inversion symmetry (even terms are not involved) and with a fixed point at x=O, that should represent the period T solution. This symmetry guarantees the existence of a period doubling bifurcation as soon as the slope at x=O becomes higher than minus one. Moreover, the map allows for the existence of other fixed points that in its second iteration might produce an inverse saddle-node bifurcation. Finally, it allows for reinjection and also to escape to infinity for high values of the control parameter. All this required the coefficient of the seventh- and fifth-order terms to be negative and positive, respectively, in order to reproduce the oscillator behavior. Here we provide complete numerical simulation results on the map that char acterize completely the aforementioned continuous transition between inter mittencies-I and -III.