Computational Model Linking Neural Activity to Behavior
There are several such models in the field of auditory perception. For example Patterson 1996 [1] suggests a model that starts with a simulation of the cochlea and the neural activity and reaches up to perception; Winkler 2006 [2] reviews the process of auditory perception, again from the cochlea up to perception.

Somewhat old and does not mention a specific model, but still a very relevant review of the neural activity - behaviour interaction debate is provided in Barlow 1972 [3]. 



[1] Patterson R.D., Holdsworth J., A functional model of neural activity patterns and auditory images‏. Advances in Speech, Hearing and Language Processing, 1996. link.

[2] Winkler I., Denham S.L., Nelken I‏., Modeling the auditory scene: predictive regularity representations and perceptual objects. Trends in cognitive sciences, 2009. doi: 10.1016/j.tics.2009.09.003

[3] Barlow B.H., Single units and sensation: A neuron doctrine for perceptual psychology? Perception, 1972. link