  Changes in brain states, as found in many neurological diseases such as
epilepsy, are often described as bifurcations in mesoscopic neural models.
Nearly all of these models rely on a mathematically convenient, but
biophysically inaccurate, description of the synaptic input to neurons called
current-based synapses. We develop a novel analytical framework to analyze the
effects of a more biophysically realistic description, known as
conductance-based synapses. These are implemented in a mesoscopic neural model
and compared to the standard approximation via a single parameter homotopic
mapping. A bifurcation analysis using the homotopy parameter demonstrates that
if a more realistic synaptic coupling mechanism is used in this class of
models, then a bifurcation or transition to an abnormal brain state does not
occur in the same parameter space. We show that the more realistic coupling has
additional mathematical parameters that require a fundamentally different
biophysical mechanism to undergo a state transition. These results demonstrate
the importance of incorporating more realistic synapses in mesoscopic neural
models and challenge the accuracy of previous models, especially those
describing brain state transitions such as epilepsy.
