What are the most common software tools you use in your day to day work in computational neuroscience?
I am referring to neuroscience tools like GENESIS and NOT to generic tools like Excel.
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Here is a comprehensive list of Computational Neuroscience Software
My opinion below comes form the perspective of nonlinear dynamics (using differential equations to model ion currents in neurons). So more the math/physics/electrical engineering approach to Computational Neuroscience (not so much the Computer Science or Psychology approach):
Personally, I don't use pre-packaged tools like NEURON or GENESIS. I take mathematical models established in literature (i.e. The Hodgkin Huxley model) and use Matlab or Python to model them. I essentially do what Neuron or Genesis does, but I do it my way so I can extract the information that's relevant to me. This is how I have been trained through physics and applied mathematics departments. To not rely on other people's implementations.
For nonlinear analysis of dynamical systems (because there's really a lot of extravagant mathematics that you don't want to just code yourself) a lot of people use XPP/AUTO, designed, in part, by Bard Ermentrout (a well-known computational neuroscientist). This is a good way to go if you're not into writing code, but I prefer a more hackable tool. I've been learning Matcont, a similar toolbox for Matlab but since it is made with m-files (matlab's data type) you can hack it and make it into code to integrate with your own Matlab software, avoiding the GUI clicking and dragging.
I work mostly with MATLAB, and if necessary C/C++. Those are generic tools, but widely used in computational neuroscience. I often analyze and model spike trains in high time resolution, and there isn't a tool that is used universally yet. I have my own set of tools that I have developed in MATLAB. Also, many others in computational neuroscience publishes their code in MATLAB or python, so that also steers the community, I think.
I tend to code my models using Python or C/C++. Using common languages, rather than proprietary (MATLAB) or specialized tools (GENESIS, Nengo, etc.) makes it much easier to share with the community. Most people know (or can quickly pick up) Python or C, whereas not everyone has access to proprietary software or the willingness/time to learn a specialized tool. And, as stated above by Xurtio, I prefer not to rely on other peoples' code.