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Full-Text Articles in Physical Sciences and Mathematics
Update Sequence Stability In Graph Dynamical Systems, Matthew Macauley, Henning S. Mortveit
Update Sequence Stability In Graph Dynamical Systems, Matthew Macauley, Henning S. Mortveit
Publications
In this article, we study finite dynamical systems defined over graphs, where the functions are applied asynchronously. Our goal is to quantify and understand stability of the dynamics with respect to the update sequence, and to relate this to structural properties of the graph. We introduce and analyze three different notions of update sequence stability, each capturing different aspects of the dynamics. When compared to each other, these stability concepts yield vastly different conclusions regarding the relationship between stability and graph structure, painting a more complete picture of update sequence stability.
Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal
Numerical Simulations Of Snake Dissipative Solitons In Complex Cubic-Quintic Ginzburg-Landau Equation, S.C. Mancas, Harihar Khanal
Publications
Numerical simulations of the complex cubic-quintic Ginzburg-Landau equation (CCQGLE), a canonical equation governing the weakly nonlinear behavior of dissipative systems in a wide variety of disciplines, reveal five entirely novel classes of pulse or solitary waves solutions, viz. pulsating, creeping, snaking, erupting, and chaotical solitons. Here, we develop a theoretical framework for analyzing the full spatio-temporal structure of one class of dissipative solution (snaking soliton) of the CCQGLE using the variational approximation technique and the dynamical systems theory. The qualitative behavior of the snaking soliton is investigated using the numerical simulations of (a) the full nonlinear complex partial differential equation …
Cycle Equivalence Of Graph Dynamical Systems, Matthew Macauley, Henning S. Mortveit
Cycle Equivalence Of Graph Dynamical Systems, Matthew Macauley, Henning S. Mortveit
Publications
Graph dynamical systems (GDSs) generalize concepts such as cellular automata and Boolean networks and can describe a wide range of distributed, nonlinear phenomena. Two GDSs are cycle equivalent if their periodic orbits are isomorphic as directed graphs, which captures the notion of having comparable long-term dynamics. In this paper, we study cycle equivalence of GDSs in which the vertex functions are applied sequentially through an update sequence. The main result is a general characterization of cycle equivalence based on the underlying graph Y and the update sequences. We construct and analyse two graphs C(Y) and D( …
On C2 -Smooth Surfaces Of Constant Width, Brendan Guilfoyle, Wilhelm Klingenberg
On C2 -Smooth Surfaces Of Constant Width, Brendan Guilfoyle, Wilhelm Klingenberg
Publications
A number of results for C2 -smooth surfaces of constant width in Euclidean 3-space E 3 are obtained. In particular, an integral inequality for constant width surfaces is established. This is used to prove that the ratio of volume to cubed width of a constant width surface is reduced by shrinking it along its normal lines. We also give a characterization of surfaces of constant width that have rational support function. Our techniques, which are complex differential geometric in nature, allow us to construct explicit smooth surfaces of constant width in E 3 , and their focal sets. They also …