  The construction of transfer functions in theoretical neuroscience plays an
important role in determining the spiking rate behavior of neurons in networks.
These functions can be obtained through various fitting methods, but the
biological relevance of the parameters is not always clear. However, for
stationary inputs, such functions can be obtained without the adjustment of
free parameters by using mean-field methods. In this work, we expand current
Fokker-Planck approaches to account for the concurrent influence of colored and
multiplicative noise terms on generic conductance-based integrate-and-fire
neurons. We reduce the resulting stochastic system from the application of the
diffusion approximation to a one-dimensional Langevin equation. An effective
Fokker-Planck is then constructed using Fox Theory, which is solved numerically
to obtain the transfer function. The solution is capable of reproducing the
transfer function behavior of simulated neurons across a wide range of
parameters. The method can also be easily extended to account for different
sources of noise with various multiplicative terms, and it can be used in other
types of problems in principle.
