Controlling chaos in the brain

Abstract

In a spontaneously bursting neuronal network in vitro, chaos can be demonstrated by the presence of unstable fixed-point behaviour. Chaos control techniques can increase the periodicity of such neuronal population bursting behaviour. Periodic pacing is also effective in entraining such systems, although in a qualitatively different fashion. Using a strategy of anticontrol such systems can be made less periodic. These techniques may be applicable to in vivo epileptic foci.

The control of chaos: theory and applications

“…et al [165]. An interesting suggestion here is that one can, in fact, try to maintain the chaotic state, which sometimes can be preferable.…”

Delay stabilization of periodic orbits in coupled oscillator systems

“…For instance, cognitive brain functions (binding problem) and pathological brain conditions, such as epilepsy and Parkinson's disease (Schiff et al 1994;Rosenblum et al 2001;Rosenblum & Pikovsky 2004;Popovych et al 2005), are related to the synchronization of neurons and neural populations. Time delays are always present in coupled systems owing to the finite signalpropagation time.…”

Attractor switching by neural control of chaotic neurodynamics

“…The basic idea is to stabilize one of the in nitely many unstable periodic orbits in a chaotic attractor by feedback control (Ott, et al, 1990). The relevance of this method for neural systems has been demonstrated for instance by Ding and Kelso (1991) (following the general ideas of Freemann), Louren co and Babloyantz (1994) (suggested for pattern recognition and motion detection), Babloyantz and Louren co (1994) (applied to biologically oriented models), and Schi , et al (1994) (applied to in vitro experiments). The basic feature of this method is that speci c oscillatory modes, which may code for instance behavior relevant stimuli, are linked by seemingly chaotic transient states.…”

“…From this data it is now evident that non-linear dynamics is fundamental for understanding higher level brain functions. In particular, chaotic dynamics is frequently observed in biological neural networks, although its functional role is still obscure (Guevara, et al, 1983Babloyantz, et al, 1985Babloyantz and Destexhe, 1986Freeman, 1988, 1992Elbert, et al, 1994Freeman and Barrie, 1994Schi , et al, 1994Hayashi and Ishizuka, 1995. One hypothesis is that chaotic dynamics endows a neural system with the ability to respond rapidly and with a exible repertoir of behaviors to a c hanging environment (Skarda andFreeman, 1987 Freeman, 1993).…”