Within computational neuroscience there seem to be two main theoretical paradigms. In the first, the brain is viewed as an elaborate and nested control system. This branch of investigation tends to use many of the same mathematical models as those used in the engineering discipline of control, albeit with an eye on the biological feasibility and possible neuronal configurations necessary for attaining such a control system. In the second, the brain is viewed as a dynamical system on the edge of chaos, and thus utilizes the mathematical tools found in dynamical system analysis. I have to admit that the latter of these two paradigms I am rather fuzzy on, despite having taken (and done rather well in) a course on Chaos, Fractals, and Dynamics. I am not sure if my inability to fathom what a 'dynamical system on the verge of chaos' means is due to a lack of intellectual capacity on my part or a lack of substance underlying the fancy terms being thrown around on the part of those championing the dynamical system interpretation. My guess is that the two paradigms are not as entirely exclusive as some claim them to be, but I think I will have to gain a better understanding of the application of dynamics to physiology before I can be sure. In the meantime, the control systems approach speaks quite clearly to the (former) engineer in me, and I find the control theory approach rather appealing. It is simple, elegant, and powerful.
Before I continue in this vein, however, I should mention a brief caveat. There is a third branch of thought which I have not included in this description known as machine learning. While it could also be argued to be a paradigm of computational neuroscience (or at least my interpretation of what computational neuroscience ought to be), I have not included it in this discussion because, to me, it is much more a branch of traditional approaches to artificial intelligence. Machine learning tends to focus more on function modeling through stochastic methods. While this provides many powerful tools (some of which are even utilized within the control systems approach), there is a lack of emphasis on physiological feasibility which might provide for a general theory of intelligence. Of course, I think many of the mathematical tricks used in machine learning (like principle components analysis (PCA)) will likely have neuronal correlates found in which our brains somehow provide a system to achieve similar results, machine learning does not tend to be devoted to uncovering methods of cognition as its primary goal.
Now that I have rambled about machine learning, I shall return to control theory. A control system is essentially any system designed to control a variable through time. The actual form the control system takes can be quite varied, including electronic control systems, mechanical ones, and, as I surmise our brains might be, electrochemical. They usually utilize some form of feedback (most often negative), since an open control system (as those without feedback are called) are not really much good at controlling anything. However, I will go into more detail about control theory in another post. This post was simply meant to introduce the idea of the different paradigms, as well as the fact that I am currently more focused on control theory.