Honors College Thesis


The Dynamics of Random Pulse-Coupled Oscillator Networks Público Deposited

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  • The pulse-coupled oscillator model is widely used to simulate the dynamics of neural systems. For networks with particular internal (Mirollo-Strogatz) dynamics, I will define three broad patterns of collective behaviors found in literature in terms of inter-spike interval (ISI) statistics. These patterns are i) temporally-regular, characterized by all oscillators in the system firing with the same average ISI, ii) chimeric, where a group of oscillators fire with the same average ISI and the others do not, and iii) temporally-irregular, where none of the oscillators fire with the same average ISI. Chimera states are of particular interest because their presence in networks of neurons with identical internal dynamics is surprising. With these definitions, I will describe the influence of network connection density, network size, and ratio of inhibitory to excitatory connections on the frequency of each pattern. Networks that are large, densely connected, and either fully excitatory or fully inhibitory tend to favor temporally-regular dynamics while smaller networks with mixed excitatory and inhibitory connections produce more temporally-irregular dynamics. In binomial random networks, chimeric dynamics are found most commonly in systems of size 100 to 200 or in smaller systems with connection densities near 0.2 and 0.8. Chimera states are most frequently produced by networks with sizes and connection densities between those which strongly promote temporally-regular and temporally-irregular dynamics suggesting that these variables may be tuned to control the dynamical pat-terns produced by random networks. Additionally, I will assess a relatively recent distance metric called the normalized compression distance (NCD) as a method of identifying and classifying dynamical patterns at the network level. This method can potentially classify system states even when the underlying system is not purely deterministic.
  • Key Words: pulse-coupled oscillators, networks, complexity
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