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chaoming0625 committed Oct 27, 2021
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14 changes: 7 additions & 7 deletions cann/Wu_2008_CANN.ipynb
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"id": "aa926f46",
"metadata": {},
"source": [
"The mathematical equation of the Continuous-attractor Neural Network (cann) is given by:\n",
"The mathematical equation of the Continuous-Attractor Neural Network (CANN) is given by:\n",
"\n",
"$$\\tau \\frac{du(x,t)}{dt} = -u(x,t) + \\rho \\int dx' J(x,x') r(x',t)+I_{ext}$$\n",
"\n",
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},
{
"cell_type": "markdown",
"id": "b463a007",
"id": "aa8cb3c4",
"metadata": {},
"source": [
"<img src=\"../images/cann-encoding.gif\">"
"![](../images/cann-encoding.gif)"
]
},
{
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},
{
"cell_type": "markdown",
"id": "db638c78",
"id": "deb96b0b",
"metadata": {},
"source": [
"<img src=\"../images/cann-decoding.gif\">"
"![](../images/cann-decoding.gif)"
]
},
{
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},
{
"cell_type": "markdown",
"id": "20fbc890",
"id": "dc4c39bf",
"metadata": {},
"source": [
"<img src=\"../images/cann-tracking.gif\">"
"![](../images/cann-tracking.gif)"
]
}
],
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8 changes: 4 additions & 4 deletions cann/Wu_2008_CANN.py
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# - Chaoming Wang ([email protected])

# %% [markdown]
# The mathematical equation of the Continuous-attractor Neural Network (cann) is given by:
# The mathematical equation of the Continuous-Attractor Neural Network (CANN) is given by:
#
# $$\tau \frac{du(x,t)}{dt} = -u(x,t) + \rho \int dx' J(x,x') r(x',t)+I_{ext}$$
#
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)

# %% [markdown]
# <img src="../images/cann-encoding.gif">
# ![](../images/cann-encoding.gif)

# %% [markdown]
# ## Template matching
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)

# %% [markdown]
# <img src="../images/cann-decoding.gif">
# ![](../images/cann-decoding.gif)

# %% [markdown]
# ## Smooth tracking
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)

# %% [markdown]
# <img src="../images/cann-tracking.gif">
# ![](../images/cann-tracking.gif)
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7 changes: 0 additions & 7 deletions neurons/Izhikevich_2003_Izhikevich_model.ipynb
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"Izhikevich neuron model reproduces spiking and bursting behavior of known types of cortical neurons. This model combines the biologically plausibility of Hodgkin–Huxley-type dynamics (HH model) and the computational efficiency of integrate-and-fire neurons (LIF model) ."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](../images/izhikevich.jfif)"
]
},
{
"cell_type": "markdown",
"metadata": {},
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5 changes: 1 addition & 4 deletions neurons/Izhikevich_2003_Izhikevich_model.py
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# extension: .py
# format_name: percent
# format_version: '1.3'
# jupytext_version: 1.11.4
# jupytext_version: 1.11.5
# kernelspec:
# display_name: brainpy
# language: python
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# %% [markdown]
# Izhikevich neuron model reproduces spiking and bursting behavior of known types of cortical neurons. This model combines the biologically plausibility of Hodgkin–Huxley-type dynamics (HH model) and the computational efficiency of integrate-and-fire neurons (LIF model) .

# %% [markdown]
# ![](../images/izhikevich.jfif)

# %% [markdown]
# Bifurcation methodologies enable us to reduce many biophysically accurate Hodgkin–Huxley-type neuronal models to a two-dimensional system of ordinary differential equations of the form:
#
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