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FARMS NETWORK

AUTHORS: Jonathan Arreguit & Shravan Tata Ramalingasetty

EMAIL: [email protected]

Description :

This respository contains the necessary components to generate, integrate, analyze and visualize neural network models. Currently the following neuron models are implemented :

  • lif_danner
  • lif_danner_nap
  • lif_daun_interneuron
  • hh_daun_motorneuron
  • sensory_neuron
  • leaky_integrator
  • oscillator
  • morphed_oscillator
  • fitzhugh_nagumo
  • matsuoka_neuron
  • morris_lecar

Installation

Requirements

  • Python 2/3
  • Cython
  • pip
  • tqdm
  • numpy
  • matplotlib
  • networkx
  • pydot
  • ddt
  • scipy
  • farms_pylog
  • farms_container

Steps for local install

The master branch is only supports Python 3. For Python 2 installation jump XXXXX

For user installation

pip install git+https://gitlab.com/farmsim/farms_network.git#egg=farms_network

For developer installation

git clone https://gitlab.com/farmsim/farms_network.git#egg=farms_network PATH_TO_THE_DIRECTORY
cd PATH_TO_THE_DIRECTORY
pip install -e . --user

For Python 2 user installation

pip install git+https://gitlab.com/farmsim/[email protected]#egg=farms_network

For Python 2 developer installation

git clone https://gitlab.com/farmsim/[email protected]#egg=farms_network PATH_TO_THE_DIRECTORY
cd PATH_TO_THE_DIRECTORY
pip install -e . --user

Example

Danner mouse network

img

Implementation of neuron models in FARMS

  1. Morris Lecar Model
    This is a two dimensional simplified version of the Hodgkin-Huxley neuron. It was first developed to reproduce the oscillatory behaviors in particular type of muscle fibers subject to change in ion channel conductance ().
    Here we consider a variation useful for nonlinear analysis given by 
    \begin{aligned} C \frac{\mathrm{d} V}{\mathrm{d} t}=& I_{\text {stim }}-g_{\text {fast }} m_{\infty}(V)\left(V-E_{\mathrm{Na}}\right)-g_{\text {slow }} w\left(V-E_{\mathrm{k}}\right) \\ &-g_{\text {leak }}\left(V-E_{\text {leak }}\right) \\ \frac{\mathrm{d} w}{\mathrm{d} t} &=\phi_{w} \frac{w_{\infty}(V)-w}{\tau_{w}(V)} \end{aligned}

    V is the fast activation variable and w is the slow recovery variable. E represents the equilibrium potential and g_{fast}, g_{slow} and g_{leak} are the conductances of corrosponding fast, slow and leak currents respectively. The steady state activation functions are given by

    \begin{aligned} m_{\infty}(V) &=0.5\left[1+\tanh \left(\frac{V-\beta_{m}}{\gamma_{m}}\right)\right] \\ w_{\infty}(V) &=0.5\left[1+\tanh \left(\frac{V-\beta_{w}}{\gamma_{w}}\right)\right] \\ \tau_{w}(V) &=\frac{1}{\cosh \left(\frac{V-\beta_{w}}{2 \gamma_{w}}\right)} \end{aligned}

    Since the system is two dimensional, phase plane analysis is easily tractable. Thus, it finds many applications in nonlinear analysis of neural dynamics for computational neuroscience ().

  2. Matsuoka Model
    This model was developed by to attempt modelling stable oscillatory behaviors that are observed in biological systems.

    The dynamics for two Matsuoka neurons with mutual inhibition is given by:

    \begin{aligned} \tau \frac{\mathrm{d}}{\mathrm{d} t} V_{i}(t)+V_{i}(t) &=c-a y_{j}(t)-b w_{i}(t) \\(i, j=&1,2 ; j \neq i) \\ T \frac{\mathrm{d}}{\mathrm{d} t} w_{i}(t)+\nu_i w_{i}(t) &=y_{i}(t) \\ y_{i}(t)=g\left(V_{i}(t) - \theta_{i} \right) & \end{aligned}

    g(.) is a piecewise linear function g(x)=\max \{0, x\} which represents the threshold property of neurons. \nu_i variable is used to capture the adaptive behavior observed in real neurons and plays a crucial role in generating stable limit cycles.

    It is observed that g has a linear behavior in a limited sense, such that g(kx) = kg(x) which simplifies the analytical treatment (covered in detail by ). Since then, this model has been widely used to model central pattern generators (, )

  3. Fitzhugh Nagumo model
    This is a two dimensional simplified model of neurons modelled by and . It closely resembles to the Van der Pol oscillator with a forcing input. The dynamics are:
    \begin{array}{l}{\dot{V}=V-\frac{V^{3}}{3}-w+I_{\mathrm{ext}}} \\ {\tau \dot{w}=V+a-b w}\end{array}

    As in Morris Lecar model, V here is a fast activation variable and w is a slow recovery variable. This model is used in the following section to study bifurcation analysis tools.