For example, in most studies of monkey vision, a visual stimulus appears if the animal directs gaze to a fixation point .

This was followed by a memory delay of two time steps during which only the fixation point was Visible.

2B) represented the color of the fixation point and the presence of the peripheral cues.

2D (upper row) was active as long as the fixation point was present and switched off when it disappeared, thus cueing the model to make an eye movement.

All tasks have a similar overall structure: the monkey starts a trial by directing gaze to a fixation point or by touching a response key.

We encouraged fixation (or touching the key in the vibrotactile task below) by giving a small shaping reward (r,, 0.2 units) if the model directed gaze to the fixation point (touched the key).

To simplify the analysis, we ignored the leak term and considered a linear transfer function, 8(2) 2 z for Which we calculated the fixed point rates 7L D1 and km.

As in the ‘additive’ scenario, we performed a simplified analysis of the dynamics of Eqs 21 and 22 without leak term and a linear transfer function and found the fixed point rates 7L D1 and

In this regime, the striatal network settles into stable fixed points (cf.

We confirmed this by evaluating the fixed points of the linearized dynamics of the D1 and D2 MSNs in a mean field model (Eqs 25—27, Fig 1B—grey and black traces).

Linearizing around the fixed point With the Iacobian ma-triX:

Where allows to analyze the stability by calculating the eigenvalues of the fixed point .

We found the ei-genvalues to be real and negative for all values of the fixed points .

Thirdly, our model explores the striatal dynamics at steady states, since the model showed stable fixed points .

(A) Fixed points for D1 and D2 MSNs plotted for different levels of dopamine.

Following the usual practice in the analysis of dynamical systems, we study the basic properties of equations (11), such as fixed points and linear stability analysis, to analyze the key features leading to heterocyst differentiation.

First, we look at the fixed points of qa and qr for each pair of values of qs and q”

The fixed points on the lower and upper branches are always stable (blue region in Fig.

a feedback loop) and their states form a partial fixed point of the Boolean model.

(A partial fixed point is a subset of nodes and a respective state for each of these nodes such that updating any node in the subset leaves its state unchanged, regardless of the state of the nodes outside the subset.)

It is noteworthy that stable motifs are preserved for other updating schemes because of their dynamical property of being partial fixed points .

The stable motifs’ states are partial fixed points of the logical model, and as such, they act as “points of no return” in the dynamics.

Thus, the fixed point attractors of the Boolean model are preserved in the ODE model.

These stable motifs are strongly connected components and partial fixed points of the logical network.