What is the relationship between IIP2, IIP3 and a1,a2,a3?

Given a system where output and input is related by y(t)=a1x(t)+a2x2(t)+a3x3(t)

What is the relationship between IIP2, IIP3 and a1,a2,a3?

Thanks

I guess you mean IP2,3 (Intercept points), right ?

If this is the case , as in an amplifier, you can use superposition to examine this relation :

If you draw the output terms seperately on a dB scale, you'll see that
a1*x(t) has a slope of 1 (10dB/dec) ,a2*x2(t) has slope=2(20 dB/dec) and a3*x3(t) has a slope=3 (30dB/dec).

You can solve the relation by equating : a1*x = a3*x3 ( which is the IP3 pt. )
or a2*x2=a1*x (which is IP2 pt. )

as far as I remember
a2 = Diode junction conductance (1/R_junction)
a3 = α(I_dc+I_sat), α=q/nKT

P.