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Full-Text Articles in Non-linear Dynamics
Stability Of Large Flocks: An Example, J. J. P. Veerman, F. M. Tangerman
Stability Of Large Flocks: An Example, J. J. P. Veerman, F. M. Tangerman
Mathematics and Statistics Faculty Publications and Presentations
The movement of a flock with a single leader (and a directed path from it to every agent) can be stabilized. Nonetheless for large flocks perturbations in the movement of the leader may grow to a considerable size as they propagate throughout the flock and before they die out over time. As an example we consider a string of N+1 oscillators moving in the line. Each one `observes' the relative velocity and position of only its nearest neighbors. This information is then used to determine its own acceleration. Now we fix all parameters except the number of oscillators. We then …
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Asymptotic Reliability Rheory Of K-Out-Of-N Systems, Nuria Torrado, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
We formulate a theory that allows us to formulate a simple criterion that ensures that two k-out-of-n systems A and are not ordered. If the systems fail the criterion, it does not follow they are ordered. Thus the theory only serves to avoid some a priori useless comparisons: when neither A nor can be said to be better than the other. The power of the theory lies in its wide potential applicability: the assumptions involve very weak estimates on the asymptotic behavior (as t→0 and as t→∞) of the constituent survival probabilities. We include examples.
Stability Of Linear Flocks On A Ring Road, J. J. P. Veerman, Carlos Martins Da Fonseca
Stability Of Linear Flocks On A Ring Road, J. J. P. Veerman, Carlos Martins Da Fonseca
Mathematics and Statistics Faculty Publications and Presentations
We discuss some stability problems when each agent of a linear flock on the line interacts with its two nearest neighbors (one on either side).