The magnitude is plotted on a logarithmic scale for easier visualization, and arrows give gradient direction. Streamlines are depicted in cyan. The nullclines of each dynamical system are shown in black. The RNI system is formulated as an extension of the tangling of nullclines in the WTA dynamics, where additional crossings of the nullclines result in stable points.</p
A) RNNs receive transient stimuli as input, along with a reference oscillation. Networks are trained...
(a) shows the nullclines of the Izhikevich neuron model in phase space (V, u) without current, RI = ...
<p>(A) Schematic diagram for attractor landscapes and state transitions of dynamical systems. Each r...
Color denotes the magnitude of the dynamics and , and the direction is shown by the arrows. Streaml...
<p>(A) Fixation (pre-target onset): , , . Orange and green curves represent nullclines: where and ,...
<p>The -nullcline and -nullcline are colored in blue and green respectively. The red circles represe...
A) Example trajectory of controlled dynamics for evidence accumulation. Nullclines and stable points...
<p>In these panels, the unperturbed behavior of the model is compared to the controlled behavior at ...
The phase portrait for dynamic systems is a tool used to graphically determine the instantaneous beh...
International audienceWe analyze a four-dimensional slow-fast piecewise linear system consisting of ...
A) Poincaré maps illustrate that the cycles of Fig 2 correspond to attractive limit cycles. Sixteen ...
Compute and draw phase portraits using Matlab or other simulation software of one or more of the fol...
<p>The top traces show the membrane potential traces of two coupled model neurons, whereas the botto...
As we strive to understand the mechanisms underlying neural computation, mathematical models are inc...
<p>Demonstrated here are four kinds of dynamics generated by a two neuron network. In the left two c...
A) RNNs receive transient stimuli as input, along with a reference oscillation. Networks are trained...
(a) shows the nullclines of the Izhikevich neuron model in phase space (V, u) without current, RI = ...
<p>(A) Schematic diagram for attractor landscapes and state transitions of dynamical systems. Each r...
Color denotes the magnitude of the dynamics and , and the direction is shown by the arrows. Streaml...
<p>(A) Fixation (pre-target onset): , , . Orange and green curves represent nullclines: where and ,...
<p>The -nullcline and -nullcline are colored in blue and green respectively. The red circles represe...
A) Example trajectory of controlled dynamics for evidence accumulation. Nullclines and stable points...
<p>In these panels, the unperturbed behavior of the model is compared to the controlled behavior at ...
The phase portrait for dynamic systems is a tool used to graphically determine the instantaneous beh...
International audienceWe analyze a four-dimensional slow-fast piecewise linear system consisting of ...
A) Poincaré maps illustrate that the cycles of Fig 2 correspond to attractive limit cycles. Sixteen ...
Compute and draw phase portraits using Matlab or other simulation software of one or more of the fol...
<p>The top traces show the membrane potential traces of two coupled model neurons, whereas the botto...
As we strive to understand the mechanisms underlying neural computation, mathematical models are inc...
<p>Demonstrated here are four kinds of dynamics generated by a two neuron network. In the left two c...
A) RNNs receive transient stimuli as input, along with a reference oscillation. Networks are trained...
(a) shows the nullclines of the Izhikevich neuron model in phase space (V, u) without current, RI = ...
<p>(A) Schematic diagram for attractor landscapes and state transitions of dynamical systems. Each r...