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Articles about computational science and data science, neuroscience, and open source solutions. Personal stories are filed under Weekend Stories. Browse all topics here. All posts are CC BY-NC-SA licensed unless otherwise stated. Feel free to share, remix, and adapt the content as long as you give appropriate credit and distribute your contributions under the same license.
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NEST simulator – A powerful tool for simulating large-scale spiking neural networks
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
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
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
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
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.
Using phase plane analysis to understand dynamical systems
When it comes to understanding the behavior of dynamical systems, it can quickly become too complex to analyze the system’s behavior directly from its differential equations. In such cases, phase plane analysis can be a powerful tool to gain insights into the system’s behavior. This method allows us to visualize the system’s dynamics in phase portraits, providing a clear and intuitive representation of the system’s behavior. Here, we explore how we can use this method and exemplarily apply it to the simple pendulum.
PyTorch on Apple Silicon
Already some time ago, PyTorch became fully available for Apple Silicon. It’s no longer necessary to install the nightly builds to run PyTorch on the GPU of your Apple Silicon machine as I described in one of my earlier posts.
Rössler attractor
Unlike the Lorenz attractor which emerges from the dynamics of convection rolls, the Rössler attractor does not describe a physical system found in nature. Instead, it is a mathematical construction designed to illustrate and study the behavior of chaotic systems in a simpler, more accessible manner. In this post, we explore how we can quickly simulate this strange attractor using simple Python code.