1,590 research outputs found
Boundedness and global exponential stability for delayed differential equations with applications
The boundedness of solutions for a class of n-dimensional differential equations with distributed delays is established by assuming the existence of instantaneous negative feedbacks which dominate the delay effect. As an important by-product, some criteria for global exponential stability of equilibria are obtained. The results are illustrated with applications to delayed neural networks and population dynamics models.POCI 2010CMATFundação para a Ciência e a Tecnologia (FCT) - SFRH/BD/29563/2006CMAFFEDE
Almost periodic solutions of retarded SICNNs with functional response on piecewise constant argument
We consider a new model for shunting inhibitory cellular neural networks,
retarded functional differential equations with piecewise constant argument.
The existence and exponential stability of almost periodic solutions are
investigated. An illustrative example is provided.Comment: 24 pages, 1 figur
Sufficient Conditions for Polynomial Asymptotic Behaviour of the Stochastic Pantograph Equation
This paper studies the asymptotic growth and decay properties of solutions of
the stochastic pantograph equation with multiplicative noise. We give
sufficient conditions on the parameters for solutions to grow at a polynomial
rate in -th mean and in the almost sure sense. Under stronger conditions the
solutions decay to zero with a polynomial rate in -th mean and in the almost
sure sense. When polynomial bounds cannot be achieved, we show for a different
set of parameters that exponential growth bounds of solutions in -th mean
and an almost sure sense can be obtained. Analogous results are established for
pantograph equations with several delays, and for general finite dimensional
equations.Comment: 29 pages, to appear Electronic Journal of Qualitative Theory of
Differential Equations, Proc. 10th Coll. Qualitative Theory of Diff. Equ.
(July 1--4, 2015, Szeged, Hungary
Global Well-Posedness and Exponential Stability for Heterogeneous Anisotropic Maxwell's Equations under a Nonlinear Boundary Feedback with Delay
We consider an initial-boundary value problem for the Maxwell's system in a
bounded domain with a linear inhomogeneous anisotropic instantaneous material
law subject to a nonlinear Silver-Muller-type boundary feedback mechanism
incorporating both an instantaneous damping and a time-localized delay effect.
By proving the maximal monotonicity property of the underlying nonlinear
generator, we establish the global well-posedness in an appropriate Hilbert
space. Further, under suitable assumptions and geometric conditions, we show
the system is exponentially stable.Comment: updated and improved versio
Eliminating flutter for clamped von Karman plates immersed in subsonic flows
We address the long-time behavior of a non-rotational von Karman plate in an
inviscid potential flow. The model arises in aeroelasticity and models the
interaction between a thin, nonlinear panel and a flow of gas in which it is
immersed [6, 21, 23]. Recent results in [16, 18] show that the plate component
of the dynamics (in the presence of a physical plate nonlinearity) converge to
a global compact attracting set of finite dimension; these results were
obtained in the absence of mechanical damping of any type. Here we show that,
by incorporating mechanical damping the full flow-plate system, full
trajectories---both plate and flow---converge strongly to (the set of)
stationary states. Weak convergence results require "minimal" interior damping,
and strong convergence of the dynamics are shown with sufficiently large
damping. We require the existence of a "good" energy balance equation, which is
only available when the flows are subsonic. Our proof is based on first showing
the convergence properties for regular solutions, which in turn requires
propagation of initial regularity on the infinite horizon. Then, we utilize the
exponential decay of the difference of two plate trajectories to show that full
flow-plate trajectories are uniform-in-time Hadamard continuous. This allows us
to pass convergence properties of smooth initial data to finite energy type
initial data. Physically, our results imply that flutter (a non-static end
behavior) does not occur in subsonic dynamics. While such results were known
for rotational (compact/regular) plate dynamics [14] (and references therein),
the result presented herein is the first such result obtained for
non-regularized---the most physically relevant---models
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