Thesis (M.S.) University of Alaska Fairbanks, 2014Transient spatiotemporal chaos was reported in models for chemical reactions and in experiments for turbulence in shear flow. This study shows that transient spatiotemporal chaos also exists in a diffusively coupled Morris-Lecar (ML) neuronal network, with a collapse to either a global rest state or to a state of pulse propagation. Adding synaptic coupling to this network reduces the average lifetime of spatiotemporal chaos for small to intermediate coupling strengths and almost all numbers of synapses. For large coupling strengths, close to the threshold of excitation, the average lifetime increases beyond the value for only diffusive coupling, and the collapse to the rest state dominates over the collapse to a traveling pulse state. The regime of spatiotemporal chaos is characterized by a slightly increasing Lyapunov exponent and degree of phase coherence as the number of synaptic links increases. In contrast to the diffusive network, the pulse solution must not be asymptotic in the presence of synapses. The fact that chaos could be transient in higher dimensional systems, such as the one being explored in this study, point to its presence in every day life. Transient spatiotemporal chaos in a network of coupled neurons and the associated chaotic saddle provide a possibility for switching between metastable states observed in information processing and brain function. Such transient dynamics have been observed experimentally by Mazor, when stimulating projection neurons in the locust antennal lobe with different odors
