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Izhikevich SNN simulated with NEST

In this post, we explore how easy it is to set up a large-scale, multi-population spiking neural network (SNN) with the NEST simulator. We simulate a simple SNN comprising two distinct populations of Izhikevich neurons, demonstrating the efficiency and flexibility of NEST and its capability to handle complex neural network simulations with ease.

Connection concepts in NEST

In the previous post, we learned about the basic concepts of the NEST simulator and how to create a simple single neuron model. This time, we will take a closer look at the connection concepts in NEST, which are crucial for building more complex neural networks.

Step-by-step NEST single neuron simulation

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While NEST is designed for large-scale simulations of neural spike networks, the underlying models are based on approximating the behavior of single neurons and synapses. Before using NEST for network simulations, it is probably helpful to first understand the basic functions of the software tool by modelling and studying the behavior of individual neurons. In this tutorial, you will learn about NEST’s concept of nodes and connections, how to set up a neuron model of your choice, how to change model parameters, which different stimulation paradigms are included in NEST and how to record and analyze the simulation results.

NEST simulator – A powerful tool for simulating large-scale spiking neural networks

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The NEST simulator is a powerful software tool designed for simulating large-scale networks of spiking neurons (SNN). It has become an essential instrument in the field of computational neuroscience, providing the capability to model, simulate, and analyze the complex dynamics of neuronal systems. And it comes with a user-friendly Python interface, facilitating the construction of neuronal networks with minimal effort.

Simulating spiking neural networks with Izhikevich neurons

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The Izhikevich neuron model that we have discussed earlier is known for its simplicity and computational efficiency as well as for its biological plausibility. The model is based on two coupled differential equations that describe the membrane potential and the recovery variable of a neuron. The model can reproduce a wide range of spiking behaviors observed in real neurons, such as regular spiking, fast spiking, chattering, and more. In this post, we explore how we can quickly set up a spiking neural network (SNN) simulation using the Izhikevich neuron model in Python.

Izhikevich model

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Computational neuroscience utilizes mathematical models to understand the complex dynamics of neuronal activity. Among various neuron models, the Izhikevich model stands out for its ability to combine biological fidelity with computational efficiency. Developed by Eugene Izhikevich in 2003, this model simulates the spiking and bursting behavior of neurons with a remarkable balance between simplicity and biological relevance. In this post, we explore the properties of the Izhikevich model, examining its application and adaptability in simulating single neuron behaviors.

Hodgkin-Huxley model

An important step beyond simplified neuronal models is the Hodgkin-Huxley model. This model is based on the experimental data of Hodgkin and Huxley, who received the Nobel Prize in 1963 for their groundbreaking work. The model describes the dynamics of the membrane potential of a neuron by incorporating biophysiological properties instead of phenomenological descriptions. It is a cornerstone of computational neuroscience and has been used to study the dynamics of action potentials in neurons and the behavior of neural networks. In this post, we derive the Hodgkin-Huxley model step by step and provide a simple Python implementation.

FitzHugh-Nagumo model

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In the previous post, we analyzed the dynamics of Van der Pol oscillator by using phase plane analysis. In this post, we will see, that this oscillator can be considered as a special case of another dynamical system, the FitzHugh-Nagumo model. The FitzHugh-Nagumo model is a simplified model used to describe the dynamics of the action potential in neurons. With a few modifications of the Van der Pol equations we can obtain the model’s ODE system. By again using phase plane analysis, we can then investigate how the dynamics of the system changes under these modifications.

Van der Pol oscillator

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In this post, we will apply phase plane analysis to the Van der Pol oscillator. The Van der Pol oscillator is a non-conservative oscillator with nonlinear damping, which was first described by the Dutch electrical engineer Balthasar van der Pol in 1920. We will explore how phase plane analysis can be used to gain insights into the behavior of this system and how it can be used to predict its long-term behavior.

Nullclines and fixed points of the Rössler attractor

After introducing phase plane analysis in the previous post, we will now apply this method to the Rössler attractor presented earlier. We will investigate the system’s nullclines and fixed points, and analyze the attractor’s dynamics in the phase space.