Controlling Neuronal Noise Using Chaos Control

1 Chaos control techniques have been applied to a wide variety of experimental systems, including magneto-elastic ribbons 1], lasers 2], chemical reactions 3], arrhythmic cardiac tissue 4], and spontaneously bursting neuronal networks 5]. An underlying assumption in all of these studies is that the system being controlled is chaotic. However, the identiication of chaos in experimental systems, particularly physiological systems, is a diicult and often misleading task 6{9]. Here we demonstrate that the chaos criteria used in a recent study 5] can falsely classify a noise-driven, non-chaotic neuronal model as being chaotic. We apply chaos control, periodic pacing, and anticontrol to the non-chaotic model and obtain results which are similar to those reported for apparently chaotic, in vitro neuronal networks 5]. We also obtain similar results when we apply chaos control to a simple stochastic system. These novel ndings challenge the claim that the aforementioned neuronal networks 5] were chaotic and suggest that chaos control techniques can be applied to a wider range of experimental systems than previously thought. Schii et al. 5] studied the ring behavior of neuronal networks in hippocampal slices of rat brain. They generated noise-like (possibly chaotic) burst-ring activity in these networks by exposing the hippocampal slices to K +-enriched artiicial cerebrospinal uid. As a simple analogue to this system, we considered the ring behavior of a noise-driven neuron. Speciically, we implemented the FitzHugh-Nagumo neuronal model (see Fig. 1 caption for details). In the present case, the model neuron was driven by both tonic and noisy inputs. The system parameter values were chosen such that the model neuron red periodically in the absence of noisy inputs. Phase-plane analysis showed that the additive noise simply caused the ring period to uctuate about its mean value. The periodic orbit was structurally preserved. There were no global bifurcations; thus, the additive noise did not induce chaos. To evaluate the presence of chaos in the aforementioned neuronal networks, Schii et al. 5] analyzed the rst-return maps of the burst interspike intervals (ISI) for diierent 2 hippocampal-slice preparations. According to their criteria, a system could be considered chaotic if its ISI time series contained recurrent sequences which approached an unstable periodic ip-saddle xed point (in the rst-return map) along a stable direction (manifold) and departed from it in an exponential fashion along a locally-linear unstable manifold. The ISI rst-return maps for the in vitro neuronal networks of Schii et al. 5] …