Nonlinear dynamics of a small biological neural network

We examine the role of chaos in a small biological central pattern generating network in which all of the neurons and their connections are known. The lobster stomatogaatric ganglion has 30 neurons, 14 of which form the pyloric central pattern generator (CPG). This CPG produces a three phase rhythm at a frequency of about 1 Hz. Although CPGs of this type can produce such rhythms entirely independent of sensory feedback or commands from higher centers, they generally produce oscillatory synchronized activity when modulated by chemical substances acting as hormones or released directly from neurons that have inputs to the ganglion. Sensory input acts to control the output of the CPG on a cycle-by-cycle basis. We demonstrate first of all that individual identified neurons that have been isolated from their synaptic inputs are low dimensional and behave chaotically over a large range of their operating regimes. The neurons can be regularized by connecting them to other neurons in the circuit with chemical or electrical synapses. We have modeled individual and small ensembles of pyloric neurons with both Hodgkin-Huxley and Hindmarsh-Rose type models. The latter has also been implemented in analogue hardware to construct electronic neurons. These electronic neurons are very similar to the biological neurons in their dynamical properties and when interfaced to the biological neurons, form hybrid circuits that can function normally with the electronic neurons taking the place of missing or damaged biological neurons. Supported by NIH, ONR, DOE and CIA.