Portland State University. Department of Mathematics and Statistics
J. J. P. Veerman
Term of Graduation
Date of Publication
Doctor of Philosophy (Ph.D.) in Mathematical Sciences
Mathematics and Statistics
1 online resource (vi, 134 pages)
This dissertation analyzes the global dynamics of 1-dimensional agent arrays with nearest neighbor linear couplings. The equations of motion are second order linear ODE's with constant coefficients. The novel part of this research is that the couplings are different for each agent. We allow the forces to depend on the relative position and relative velocity (damping terms) of the agents, and the coupling magnitudes differ for each agent. Further, we do not assume that the forces are "Newtonian'" (i.e., the force due to A on B equals minus the force of B on A) as this assumption does not apply to certain situations, such as traffic modeling. For example, driver A reacting to driver B does not imply the opposite reaction in driver B.
There are no known analytical means to solve these systems, even though they are linear. Relatively little is known about them. To estimate system behavior for large times we find an approximation for eigenvalues that are near the origin. The derivation of the estimate uses (generalized) periodic boundary conditions. We also present some stability conditions. Finally, we compare our estimate to simulated flocks.
© 2021 Robert G. Lyons
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Lyons, Robert G., "Linear Nearest Neighbor Flocks With All Distinct Agents" (2022). Dissertations and Theses. Paper 5903.
Available for download on Thursday, February 02, 2023