Simple Noise-Induced Transitions in Models of Neural Systems

Abstract

Two neural systems whose measured activity is aperiodic are described, along with corresponding models that shed light on the dynamical origin of this activity. Both models include noise and operate near a bifurcation. The large ongoing fluctuations in the human pupil light reflex can be studied by bringing this control system near a Hopf bifurcation. Numerical simulation of a physiologically relevant model, framed in terms of a differential-delay equation in one variable, reveals that these fluctuations can arise through the coupling of this system to colored neural noise. An interesting finding is that not only multiplicative but also additive noise can postpone this Hopf bifurcation. The other neural systems we discuss are transducer neurons. We argue that the nervous system uses noise-induced firing to achieve stimulus detection and therefore relies on noise for stimulus encoding. This is discussed in the context of sensory neurons driven by either external periodic stimuli, such as those involved in tactile and auditory transduction, or by internal periodic rhythms, such as those involved in cold thermoreception. Preliminary results from an ionic model for a cold receptor reveal that this sensory transducer relies on bursting behavior in the lower temperature range and on noise-induced firing in the higher temperature range.