Recent advances in ultrafast, ultra-short solid-state lasers have resulted in sub-6 fs pulses generated directly from the cavity of Ti:sapphire lasers. The generation of extremely short pulses is possible due to the formation of a quasi-Schrodinger soliton. Our investigation is directed to the peculiarities of the transition between femtosecond to picosecond generation. We found that the above transition is accompanied by the threshold and hysteresis phenomena. On the basis of soliton perturbation theory, the numerical simulation studying two different experimental situations has been performed, the first situation corresponds to the study of the lasers field's parameters under variation of control parameters (dispersion or pump power), the second one is for continuous variation of control parameter within a single generation session. Physically it corresponds to not repeated laser session but the variation of control parameter when the pulse has formed already.