Stability and Bifurcation Analysis of a Nonlinear DDE
Model for Drilling |
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Authors: | Email author" target="_blank">E?StoneEmail author SA?Campbell |
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Institution: | (1) Department of Mathematics and Statistics, Utah State University, Logan, UT 84322-3900, USA;(2) Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada |
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Abstract: | We discuss several examples of synchronous dynamical phenomena in
coupled cell networks
that are unexpected from symmetry considerations, but are natural
using a theory developed by Stewart, Golubitsky, and Pivato. In particular
we demonstrate patterns of synchrony in networks with small numbers of cells
and in lattices (and periodic arrays) of cells that cannot readily be
explained by conventional symmetry considerations. We also show that
different types of dynamics can coexist robustly in single solutions of
systems of coupled identical cells. The examples include a
three-cell system exhibiting equilibria, periodic, and quasiperiodic states
in different cells; periodic $2n\times 2n$ arrays of cells that generate
$2^n$ different patterns of synchrony from one symmetry-generated solution;
and systems exhibiting multirhythms (periodic solutions with rationally
related periods in different cells). Our theoretical results include the
observation that reduced equations on a center manifold of a skew product
system inherit a skew product form. |
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Keywords: | |
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