Tsodyks_synapse

[Thanh-Binh]

Describe the bug
from my best point of view, codes in the header file "tsodyks_synapse.h" from the line 259 to 281 are not correct
double Puu = ( tau_fac_ == 0.0 ) ? 0.0 : std::exp( -h / tau_fac_ );
double Pyy = std::exp( -h / tau_psc_ );
double Pzz = std::expm1( -h / tau_rec_ );
double Pxy = ( Pzz * tau_rec_ - ( Pyy - 1.0 ) * tau_psc_ ) / ( tau_psc_ - tau_rec_ );

double z = 1.0 - x_ - y_;

// propagation t_lastspike_ -> t_spike
// don't change the order !

u_ *= Puu;
x_ += Pxy * y_ - Pzz * z;
y_ *= Pyy;

// delta function u
u_ += U_ * ( 1.0 - u_ );

Those codes implement the solution of some differential equations in the paper of Tsosyks 2000:
dx/dt = z/tau_rec - u * x * delta_function(t - tsp) (1)
dy/dt = -y/tau_psc + u * x * delta_function(t - tsp) (2)
dz/dt = y/tau_psc - z / tau_rec (3)
du/dt = -u/tau_fac + U * (1-u) * delta_function(t - tsp) (4)

from (1) + (3):
dx/dt + dz/dt = y/tau_psc - uxdelta_function(t-tsp)

(2) -> dx/dt + dz/dt = -dy/dt
-> dz/dt = -dx/dt - dy/dt
-> z = z0 - x - y
where z0 is z(t = tsp)

Any explain?

[janskaar]

I don't quite follow your last step. Note that dx/dt + dy/dt + dz/dt = 0, so the sum x + y + z never changes, and in the model it is assumed to be 1.

If you integrate dz/dt = -dx/dt - dy/dt from 0 to t, you end up with z(t) = -x(t) - y(t) + x(0) + y(0) + z(0). Since the sum over the last three terms is 1, you end up with z = 1 - x - y.

[Thanh-Binh]

@janskaar OK understood, thanks.