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Full-Text Articles in Non-linear Dynamics
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
A Primer On Laplacian Dynamics In Directed Graphs, J. J. P. Veerman, R. Lyons
Mathematics and Statistics Faculty Publications and Presentations
We analyze the asymptotic behavior of general first order Laplacian processes on digraphs. The most important ones of these are diffusion and consensus with both continuous and discrete time. We treat diffusion and consensus as dual processes. This is the first complete exposition of this material in a single work.
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Stability Of A Circular System With Multiple Asymmetric Laplacians, Ivo Herman, Dan Martinec, J. J. P. Veerman, Michael Sebek
Mathematics and Statistics Faculty Publications and Presentations
We consider an asymptotic stability of a circular system where the coupling Laplacians are different for each state used for synchronization. It is shown that there must be a symmetric coupling in the output state to guarantee the stability for agents with two integrators in the open loop. Systems with agents having three or more integrators cannot be stabilized by any coupling. In addition, recent works in analysis of a scaling in vehicular platoons relate the asymptotic stability of a circular system to a string stability. Therefore, as confirmed by simulations in the paper, our results have an application also …
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Semicontinuity Of Dimension And Measure For Locally Scaling Fractals, L. B. Jonker, J. J. P. Veerman
Mathematics and Statistics Faculty Publications and Presentations
The basic question of this paper is: If you consider two iterated function systems close to one another in an appropriate topology, are the dimensions of their respective invariant sets close to one another? It is well-known that the Hausdorff dimension (and Lebesgue measure) of the invariant set do not depend continuously on the iterated function system. Our main result is that (with a restriction on the ‘non-conformality’ of the transformations) the Hausdorff dimension is a lower semi-continuous function in the C1- topology of the transformations of the iterated function system. The same question is raised of the …
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
On 2-Reptiles In The Plane, Sze-Man Ngai, Víctor F. Sirvent, J. J. P. Veerman, Yang Wang
Mathematics and Statistics Faculty Publications and Presentations
We classify all rational 2-reptiles in the plane. We also establish properties concerning rational reptiles in the plane in general.