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There is increased interest in using microphone arrays in a variety of audio source separation and consequently speech processing applications. In particular, small arrays of two to four microphones a...
This work presents an explicit formula for determining the radius of a limit cycle which is born in a Hopf bifurcation in a class of first order constant coefficient differential-delay equations. The ...
This paper investigates the dynamics of a new model of two coupled relaxation oscilla-tors. The model replaces the usual DDE (differential-delay equation) formulation with a discrete-time approach wit...
Periodic motions in DDE (Differential-Delay Equations) are typically 4 created in Hopf bifurcations. In this chapter we examine this process from several 5 points of view. Firstly we use Lindstedt’s p...
For linear systems with delays, we define a new class of Lyapunov-like functionals that may be used to prove stability. We also show how we may design a stabilizing (delayed) state feedback for delay ...
We consider solutions of the KPP-type equations with a periodically varying reaction rate, and compactly supported initial data. It has been shown by Bramson [5, 6] in the case of the constant reactio...
We consider solutions of the KPP equation with a time-dependent diffusivity of the formσ(t/T). For an initial condition that is compactly supported, we show that when σ(s) is increasing in time the fr...
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Ly...
In this paper we consider a multi-dimensional wave equation with dynamic boundary conditions related to the Kelvin-Voigt damping and a delay term acting on the boundary. If the weight of the delay ter...
In this paper, existence of S-asymptotically ω-periodic mild solutions for abstract integro-differential equationwith fractional order is considered. The main results are obtained bythe contraction ma...
Up to now, the stability problem of mild solution for the impulsive stochastic system with Poisson jumps has not been solved. In this paper, based on fixed point theory, the stability of mild solution...
Abstract: A new, improved split-step backward Euler (SSBE) method is introduced and analyzed for stochastic differential delay equations(SDDEs) with generic variable delay. The method is proved to be ...
Two identical chaotic oscillators that are mutually coupled via time delayed signals show very complex patterns of completely synchronized dynamics including stationary states and periodic as well as ...
Based on the fixed point theory, the asymp totical stability of mild solution to impulsive stochastic partial differential equations with infinite delays and Markovian jumps is studied. In addition, s...
Explicit numerical methods based on Lax-Friedrichs and Leap-Frog finite difference approximations are constructed to find the numerical solution of the first-order hyperbolic partial differential equa...

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