A considerable ammount of the world's (scarce) scientific research funds has been allocated to the search for **meaningfull** chaotic patterns in many fields, from hard sciences (e.g., physical sciences, engineering) to socioeconomic studies, with a wide range of promising and practical results. It appears that some of the tools of the science of nonlinear dynamics (and chaos) are also well-suited for studies of biological phenomena, neuroscience included. Indeed, such complex systems can give rise to collective behaviors which are not simply the sum of their components and involve huge conglomerations of related units constantly interacting with the environment. There's somewhat of a consensus that the activities undergone by neurons, neuronal assemblies and entire behavioral patterns (e.g., after epileptic seizures), the linkage between them, and their evolution over time, cannot be understood in all its complexity and practical potential without these nonlinear techniques.

As an example, take the now classic Hindmarsh & Rose mathematical model of neuronal bursting using 3 coupled first-order differential equations. A computer-simulated train of action potentials results in a pattern that would be interpreted as random on the basis of classical statistical methods, while a representation of interspike intervals reveals a well-ordered underlying generating mechanism (i.e., peak-to-peak dynamics). Rather naturally, the identification of nonlinear dynamics and chaos in an experimental neuronal setup is a very difficult task at various levels, far from the "clean" low dimensional chaos produced by computer/mathematical models. Firstly, there's lack of stationarity on the recorded signals, meaning that all the "parameters" of the (biological) system rarely remain with a constant mean and variance during measurements. This creates a not always viable need for prolonged and stable periods of observation. Secondly, collected observations generally exhibit a complex **mixture** of fluctuations beyond the system itself, including those by the environment and those by the measurement equipment. For these purposes it's helpful to start investigations by constructing a phase space description of the underlying phenomenon (i.e., phase space reconstruction and embedding of a time series), usually plotting the relationship between successive events or time intervals (i.e., a PoincarĂ© map), as most of the relevant signals are discrete ones.

And so what? Is that just public/media curiosity? In the light of the aforementioned technical difficulties neurobiologists have become gradually more interested in practical issues such as the comparison of dynamics of neuronal assemblies in various experimental conditions. With these less ambitious expectations, average (nonlinear) forecastings (e.g., of epileptic seizures) has been achieved in spike trains (demonstrating determinism as a byproduct). Alternativelly, the search for Unstable Periodic Orbits (UPOs) in the reconstructed phase spaces has been fruitful, which (paradoxically) results in an advantage if you desire to control a neuronal system to explore a large region of its phase space using only a weak control signal. Recipe: Apply a (weak) control signal to force the system to follow closely any one of the identified UPOs, obtaining large changes in the long-term behavior with minimal effort - i.e., you can select a given behavior from an "infinite" set and, if necessary, switch between them. Potential is unequivocal: Some abnormalities of neuronal systems, ranging from differing periodicities to irregular "noise-like" phenomena could define a group of "dynamical deseases" of the brain.

Think of the 50x10^6+ epileptic people worldwide, ~20% of them not sufficiently helped by medications, taking the surgical removal of the seizure-focus as the last resort. Implants who (electrically) stimulate the vagal nerve has also been used, but their action mechanism is uncertain, they have several side effects, and they could potentially kindle new epileptic foci in the area. Chaos control techniques might be used, with the advantage of requiring relatively **infrequent** stimulation of the tissue.