Nonlinear Cooperative Dynamics of Living Neurons

There is a substantial body of experimental evidence that neurons often produce oscillations to achieve their functional goals. They thus behave as dynamical systems despite the fluctuations we observe due to environmental noise and imperfections in their construction. In observations of neural behavior these oscillations can appear "intrinsic" as in the rhythmical pulsing of Central Pattern Generators (CPGs) or the oscillations can arise in response to a stimulus as in the actions of projection neurons in olfactory operation or even in the dynamical response of cortex neurons. When assemblies of neurons perform oscillations, their collective behavior is determined in an essential way by both the nonlinear dynamics of the individuals in the assembly and by the architecture of the neural circuitry. The neurons inside an assembly can synchronize, possibly with an evident time lag, to produce particular patterns which control the rhythmic muscular activity of an animal, as in CPG operation. The component neurons may compete with each other in a dynamical fashion to solve the problem of pattern recognition, as in the cortex. They may collectively produce rich spatiotemporal behavior in response to specific forms of stimulus from sensory systems. This is a review of these phenomena which are discussed in language familiar in the description of nonlinear dynamical systems including synchronization and competition. We illustrate our ideas with data from experiment and model simulations for both individual neurons and assemblies of neurons.