[R] Technological/Logistic Substitution Model

[Peter Maclean]

Any one with an idea of estimating the Technological/Logistic substitution model. The model is specified as:
fi(t(j)) = 1/[1-exp(-alpa(t(i))-beta(i)]    for t <tb and alpha >0
fi(t(j)) = 1-sum(f(j-1))- sum(f(j+1))       for tb <=t <= tc
fi(t(j)) = 1/[1+ exp(alpas(t(i)-betas(i))]  for t >=tc and alphas >0.
 
The models assume that n technologies are introduced to the market, where 1 is the oldest and technology n is the newest, i and j are subscripts representing the type of technology, fi is the market share, t is a subscript denoting time, alpha, alphas, beta, and betas are parameters, tb and tc are time periods during which the technology i starts to enter the saturation and decline phase, respectively.
 
Any suggestion, reading is helpful.  

Peter Maclean
Department of Economics
UDSM