Flicker

Inhibitory

$a_{ii}$

$a_{ie}$

$\tau_i$

$\theta_i$

$g_i$

$\sigma_{ix}$

$\sigma_{iy}$

$N_i$

$\gamma_{ii}$

$\gamma_{ie}$

Excitatory

$a_{ee}$

$a_{ei}$

$\tau_e$

$\theta_e$

$g_e$

$\sigma_{ex}$

$\sigma_{ey}$

$N_e$

$\gamma_{ee}$

$\gamma_{ei}$

Time stepping

$\Delta t$

Skip

Stimulus

$A$

Presets

E-cell firing rate ∈[0,1]

I-cell firing rate ∈[0,1]

E/I trajectories in phase space
Peripheral region

E-cell firing rate

I-cell firing rate

E/I trajectories in phase space
Stimulated region

Click to start

Wave State Demonstration

This demonstration is designed to illustrate a hypotehtical wave mode seen during optogentic stimulation in motor cortex. In this mode, the stimulated region forces damped traveling waves in the periphery at a ratio of 2:1. Additionally, there is instability inside the stimulated region, leading to traveling waves across the stimulation area that originate at the boundary. The Stimulated region has a radius of 30 pixels, the stimulus mask has been smoothed with a Gaussian kernel with a standard deviation of 4 piexls, given the stimulated region a soft boundary. Heterogeneity is added to the time constants (in a somewhat hacked way that I can explain or try to clean up), and is also smoothed with a Gaussian kernel of 4 pixels. These new additions are not reflected in the equations.

Simulation

\[\textrm{E-cells: } \tau_e \dot{U_e} = -U_e + f( (1+\gamma_{ee} S(t)) a_{ee} \cdot K_e \star U_e - (1+\gamma_{ie} S(t)) a_{ie} \cdot K_i \star U_i - \theta_e + g_e S(t) )\] \[\textrm{I-cells: } \tau_i \dot{U_i} = -U_i + f( (1+\gamma_{ei} S(t)) a_{ei} \cdot K_e \star U_e - (1+\gamma_{ii} S(t)) a_{ii} \cdot K_i \star U_i - \theta_i + g_i S(t) )\] \[\textrm{Interaction kernel (normalized to 1): } K_{e,i}(x,y) \propto \exp(\frac{1}{2} \frac{x^2}{\sigma_{x\,e,i}^2}+\frac{1}{2} \frac{y^2}{\sigma_{y\,e,i}^2})\]