Differential pair with dynamic resistance

Hi,
I need to calculate and draw asymptotes on the oscilloscope.

The tested system looks as follows:

One change - Rc = 20k Ohms.
I know that for voltage Ub1 in range for +-0.1V (approximately) transistor T2 is in the active mode. And i notice that Uwy1 is constant and this voltage is 5V. So transistor T1 is in cut-off mode. But i don't know how T2 transistor works when Ub1 voltage is less than -0.1V and when Ub1 voltage is greater than 0.1V. Does it work in saturation mode? Could you explain me?
Thanks for the help in advance!

Basically 3Vt (≈80mV) is an input differential voltage range of a BJT diff pair (you can check math analysis in Grey, Hurst, Meyer book "Analysis and design...").
If Vin_diff is higher than this 3Vt value one guy is cut-off, while second is saturated.

However, If your Re is 2.5kΩ, Rc is 20kΩ, input common mode is on ground, VEE is -5.7V and VCC is 12V, then your amplifier is in trouble.
Only left guy might be in active-linear mode, right is always squeezed by large Rc resistor.
So, for input voltage below ground, output is going to be ca Vcc-(Vcc-Vee-Vcesat)Rc/(Rc+Re), while in opposite situation, output is pulled up by Rc to Vcc.

Also, your question is not fully clear. Attached scope screenshot is in time domain and I believe it is showing full range response.
So, asymptotes of what you need?

T2 is not saturated with Rc=2k, only with 20k.

I forgot to mention that the system is powered by a current source IE = 1.5mA. And now I noticed that I sent the wrong layout. The following is correct:

Okay, it's correct electronic circuit:
and it's my assumptions and calculations:
T1 is cut-off and T2 is saturated then output voltage Uwy2 is approximately -1V.
My calculation:
Ucc-Ic*Rc+UBC2=0
UBC2-voltage base-collector on transistor T2
UBC2=0.5V because UCE=UCEsat=0.2V and UBE=0.7V
Then Ic=0.275mA
Next Uwy2=UCC-Ic*Rc=-0.5V
Is it OK? My calculations do not differ much from the oscilloscope, but I don't know if I do it correctly...

You new schematic doesn't even give a value for Rc. How could we answer?

As previously mentioned, saturation occurs above a certain value of Rc. Usually, saturation would be avoided. But it's not clear waht you want to achieve.