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lenasal committed Oct 27, 2023
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33 changes: 14 additions & 19 deletions examples/example-0-aln-minimal/index.html

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14 changes: 5 additions & 9 deletions examples/example-0.1-hopf-minimal/index.html

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2 changes: 1 addition & 1 deletion examples/example-0.3-fhn-minimal/index.html
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<h1 id="the-fitz-hugh-nagumo-oscillator">The Fitz-Hugh Nagumo oscillator</h1>
<p>In this notebook, the basic use of the implementation of the Fitz-Hugh Nagumo (<code>fhn</code>) model is presented. Usually, the <code>fhn</code> model is used to represent a single neuron (for example in <code>Cakan et al. (2014)</code>, "Heterogeneous delays in neural networks"). This is due to the difference in timescales of the two equations that define the FHN model: The first equation is often referred to as the "fast variable" whereas the second one is the "slow variable". This makes it possible to create a model with a very fast spiking mechanism but with a slow refractory period. </p>
<p>In this notebook, the basic use of the implementation of the FitzHugh-Nagumo (<code>fhn</code>) model is presented. Usually, the <code>fhn</code> model is used to represent a single neuron (for example in <code>Cakan et al. (2014)</code>, "Heterogeneous delays in neural networks"). This is due to the difference in timescales of the two equations that define the FHN model: The first equation is often referred to as the "fast variable" whereas the second one is the "slow variable". This makes it possible to create a model with a very fast spiking mechanism but with a slow refractory period. </p>
<p>In our case, we are using a parameterization of the <code>fhn</code> model that is not quite as usual. Inspired by the paper by <code>Kostova et al. (2004)</code> "FitzHugh–Nagumo revisited: Types of bifurcations, periodical forcing and stability regions by a Lyapunov functional.", the implementation in <code>neurolib</code> produces a slowly oscillating dynamics and has the advantage to incorporate an external input term that causes a Hopf bifurcation. This means, that the model roughly approximates the behaviour of the <code>aln</code> model: For low input values, there is a low-activity fixed point, for intermediate inputs, there is an oscillatory region, and for high input values, the system is in a high-activity fixed point. Thus, it offers a simple way of exploring the dynamics of a neural mass model with these properties, such as the <code>aln</code> model.</p>
<p>We want to start by producing a bifurcation diagram of a single node. With <code>neurolib</code>, this can be done with a couple of lines of code, as seen further below.</p>
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6 changes: 3 additions & 3 deletions examples/example-0.5-kuramoto/index.html
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<h1 id="single-node-simulation">Single node simulation</h1>
<p>Here we will simulate a signal node with no noise. We then cap the phase values to be between 0 and 2*pi. We also willo plot the phase values over time.</p>
<p>Here we will simulate a signal node with no noise. We then cap the phase values to be between 0 and 2*pi. We also will plot the phase values over time.</p>
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<p>Here we simulate networks of oscillators. We will simulate a network of 8 oscillators with a global coupling strength 0.3. Here we initialize a connectivity matrix with all-to-all connectivity. We then simulate the network for 30 miliseconds assuming dt is in ms. We will also plot the phase values over time.</p>
<p>Here we simulate networks of oscillators. We will simulate a network of 8 oscillators with a global coupling strength 0.3. Here we initialize a connectivity matrix with all-to-all connectivity. We then simulate the network for 30 milliseconds assuming dt is in ms. We will also plot the phase values over time.</p>
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<p>Now the syncrhonization happens after 7 ms which is faster compared to the previous simulation.</p>
<p>Now the synchronization happens after 7 ms which is faster compared to the previous simulation.</p>
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71 changes: 24 additions & 47 deletions examples/example-0.6-external-stimulus/index.html

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