Nonlinear regression with dummie variables

Question

I am creating several models, to then make the selection based on Aicc. Among these models that I am creating, I have a categorical predictive variable (fire) that I need to include in the nonlinear regression model. The three models I need to run are:

fire_vertical <- nls(R~0.23-exp(A*lnNt+C)+d*fire,
                     start=list(A=-0.33,C=0.45,d=-0.001),trace=T)

fire_lateral <- nls(R~0.23-exp((A*lnNt)+(C+d*fire)),
                    start=list(A=-0.33,C=0.45,d=-0.001),trace=T)

fire_nonlinear <- nls(R~0.23-exp((A+d*fire)*lnNt+C),
                      start=list(A=-0.33,C=0.45,d=-0.001),trace=T)

Considering the following data:

R <- c(0.02,0.00,-0.06,0.11,0.06,0.00,-0.05,-0.06,
       0.02,-0.26,0.00,0.07,-0.07,0.23,0.06,-0.14,-0.04,
       0.09,-0.09,0.09,-0.02)

lnNt <- c(6.14,6.14,5.76,6.42,6.81,
          6.81,6.49,6.14,6.24,4.81,4.81,5.14,
          4.81,6.03,6.42,5.59,5.39,5.90,5.39,5.90,5.76)

fire <- c("before","before","before",
          "before","before","before",
          "before","afterone","afterone","afterone",
          "afterone","afterone","afterone","afterone",
          "aftertwo","aftertwo","aftertwo","aftertwo","aftertwo",
          "aftertwo","aftertwo")

Where lnNt is a continuous predictive variable, while fire is a categorical predictor with three levels: before, afterone, aftertwo. I need to transform the fire into a dummie variable and make the three models presented spin this way.

Anyone who can help, I’d like to thank.