Preventing shorts and power failures

I built the circuit from my last post (Or you can find here 12V ve 5V 600ma IRF9530 Mosfetli Akım sınırlama Devresi – Elektronik Devreler Projeler). Worked like a Charm. Added a couple of LEDs to monitor if it was in normal mode or in overcurrent protection (One at the Gate and one at the Drain of T2, plus 1K resistors in series).

I understad the basic working principle of this circuit: when the voltage drop in R1 is bigger tha 0.7V, T1 starts sto conduct and shuts T2 off. Thats the easy part.

What I do not get is the role of the two capacitors. Any ideas?

C1 is quite big, and and of the drawbacks of this solutions is that it has quite a big charge after plugging it off from the power source.