STOCHASTIC CHAOS IN A NEURONAL MODEL

Abstract

Neuronal firing is one of the main information carriers in nervous systems. It has been reported that highly fluctuating, aperiodic "noise-like" inputs, similar to those occurring in areas of nervous systems, evoke reliable firing. To explain this surprising result it has been suggested that (i) the high frequency components of such inputs or a resonance phenomenon are responsible for reliable firing, with (ii) internal biophysical noise being the potential major inherent source of unreliability. Conversely, the present study shows that such fluctuating inputs do not always lead to reliability, even in the absence of noise. Using the noise-free FitzHugh–Nagumo model, we demonstrate a regime in which reliable firing never occurs. To analyze the changes responsible for unreliable firing we use methods from the Random Dynamical Systems theory. This is done through careful numerical investigations since no analytical solutions are known to our system. More precisely, from the observation that the stationary distributions remained qualitatively unchanged throughout the area of interest we conclude that the switch from reliable to unreliable firing is not associated to a phenomenological stochastic bifurcation. However, this change of behavior corresponded to a dynamical stochastic bifurcation, with the leading Lyapunov exponent of the system becoming positive. The bifurcation resulted also in a change of the stochastic attractor from a single stochastic equilibrium to one reminiscent of a strange attractor. The combination of these results lead us to argue that the unreliable firing results from stochastic chaos, and that such a phenomenon may limit the reliability of neurons in nervous systems.