30,133 research outputs found
Fast generation of stability charts for time-delay systems using continuation of characteristic roots
Many dynamic processes involve time delays, thus their dynamics are governed
by delay differential equations (DDEs). Studying the stability of dynamic
systems is critical, but analyzing the stability of time-delay systems is
challenging because DDEs are infinite-dimensional. We propose a new approach to
quickly generate stability charts for DDEs using continuation of characteristic
roots (CCR). In our CCR method, the roots of the characteristic equation of a
DDE are written as implicit functions of the parameters of interest, and the
continuation equations are derived in the form of ordinary differential
equations (ODEs). Numerical continuation is then employed to determine the
characteristic roots at all points in a parametric space; the stability of the
original DDE can then be easily determined. A key advantage of the proposed
method is that a system of linearly independent ODEs is solved rather than the
typical strategy of solving a large eigenvalue problem at each grid point in
the domain. Thus, the CCR method significantly reduces the computational effort
required to determine the stability of DDEs. As we demonstrate with several
examples, the CCR method generates highly accurate stability charts, and does
so up to 10 times faster than the Galerkin approximation method.Comment: 12 pages, 6 figure
Asymptotic properties of the spectrum of neutral delay differential equations
Spectral properties and transition to instability in neutral delay
differential equations are investigated in the limit of large delay. An
approximation of the upper boundary of stability is found and compared to an
analytically derived exact stability boundary. The approximate and exact
stability borders agree quite well for the large time delay, and the inclusion
of a time-delayed velocity feedback improves this agreement for small delays.
Theoretical results are complemented by a numerically computed spectrum of the
corresponding characteristic equations.Comment: 14 pages, 6 figure
Brownian Molecules Formed by Delayed Harmonic Interactions
A time-delayed response of individual living organisms to information
exchanged within flocks or swarms leads to the emergence of complex collective
behaviors. A recent experimental setup by (Khadka et al 2018 Nat. Commun. 9
3864), employing synthetic microswimmers, allows to emulate and study such
behavior in a controlled way, in the lab. Motivated by these experiments, we
study a system of N Brownian particles interacting via a retarded harmonic
interaction. For , we characterize its collective behavior
analytically, by solving the pertinent stochastic delay-differential equations,
and for by Brownian dynamics simulations. The particles form
molecule-like non-equilibrium structures which become unstable with increasing
number of particles, delay time, and interaction strength. We evaluate the
entropy and information fluxes maintaining these structures and, to
quantitatively characterize their stability, develop an approximate
time-dependent transition-state theory to characterize transitions between
different isomers of the molecules. For completeness, we include a
comprehensive discussion of the analytical solution procedure for systems of
linear stochastic delay differential equations in finite dimension, and new
results for covariance and time-correlation matrices.Comment: 36 pages, 26 figures, current version: further improvements and one
correctio
Canard explosion in delayed equations with multiple timescales
We analyze canard explosions in delayed differential equations with a
one-dimensional slow manifold. This study is applied to explore the dynamics of
the van der Pol slow-fast system with delayed self-coupling. In the absence of
delays, this system provides a canonical example of a canard explosion. We show
that as the delay is increased a family of `classical' canard explosions ends
as a Bogdanov-Takens bifurcation occurs at the folds points of the S-shaped
critical manifold.Comment: arXiv admin note: substantial text overlap with arXiv:1404.584
Congestion at airports: the economics of airport expansions
Congestion and subsequent delays have been prevalent in many U.S. airports in recent years. A common response to congestion, championed by many community leaders, is to expand capacity by constructing new runways and terminals. Airport expansions are costly, complex, and controversial. We begin by using basic economic theory to analyze congestion at those airports that are part of an air transportation system. Next, we describe how benefit-cost analysis is used to assess the desirability of airport expansions. Many of the key points are illustrated in the context of Lambert–St. Louis International Airport. We also examine two especially controversial aspects of expansions—the displacement of people and businesses and the effects of airport noise. Finally, we discuss congestion-based pricing of landing fees as an alternative to airport expansions.Airports ; Economic development
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