Stability of solutions to delay differential equations with periodic coefficients of linear terms.
By means of the fixed-point methods and the properties of the -pseudo almost periodic functions, we prove the existence, uniqueness, and exponential stability of the -pseudo almost periodic solutions for some models of recurrent neural networks with mixed delays and time-varying coefficients, where is a positive measure. A numerical example is given to illustrate our main results.
We present a result on the stability of moving invariant manifolds of nonlinear uncertain impulsive differential-difference equations. The result is obtained by means of piecewise continuous Lyapunov functions and a comparison principle.
We study stability switches for some class of delay differential equations with one discrete delay. We describe and use a simple method of checking the change of stability which originally comes from the paper of Cook and Driessche (1986). We explain this method on the examples of three types of prey-predator models with delay and compare the dynamics of these models under increasing delay.
This paper analyzes the BIBO stability of fractional exponential delay systems which are of retarded or neutral type. Conditions ensuring stability are given first. As is the case for the classical class of delay systems these conditions can be expressed in terms of the location of the poles of the system. Then, in view of constructing robust BIBO stabilizing controllers, explicit expressions of coprime and Bézout factors of these systems are determined. Moreover, nuclearity is analyzed in a particular...
A parameter dependent nonlinear differential-delay equation in a Banach space is investigated. It is shown that if at the critical value of the parameter the problem satisfies a condition of linearized stability then the problem exhibits a stability which is uniform with respect to the whole range of the parameter values. The general theorem is applied to a diffusion system with applications in biology.
We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the above-mentioned...
We intend to conduct a fairly complete study on Timoshenko beams with pointwise feedback controls and seek to obtain information about the eigenvalues, eigenfunctions, Riesz-Basis-Property, spectrum-determined-growth-condition, energy decay rate and various stabilities for the beams. One major difficulty of the present problem is the non-simplicity of the eigenvalues. In fact, we shall indicate in this paper situations where the multiplicity of the eigenvalues is at least two. We build all the...
A class of nonlinear simple form differential delay equations with a -periodic coefficient and a constant delay is considered. It is shown that for an arbitrary value of the period , for some , there is an equation in the class such that it possesses an asymptotically stable -period solution. The periodic solutions are constructed explicitly for the piecewise constant nonlinearities and the periodic coefficients involved, by reduction of the problem to one-dimensional maps. The periodic solutions...
In economic systems, reactions to external shocks often come with a delay. On the other hand, agents try to anticipate future developments. Both can lead to difference-differential equations with an advancing argument. These are more difficult to handle than either difference or differential equations, but they have the merit of added realism and increased credibility. This paper generalizes a model from monetary economics by von Kalckreuth and Schröder. Working out its stability properties, we...
The problem of finding an input-output representation of a nonlinear state space system, usually referred to as the state elimination, plays an important role in certain control problems. Though, it has been shown that such a representation, at least locally, always exists for both the systems with and without delays, it might be a neutral input-output differential equation in the former case, even when one starts with a retarded system. In this paper the state elimination is therefore extended...
We obtain the existence and uniqueness of square-mean pseudo almost automorphic mild solutions to first-order partial neutral stochastic functional differential equations with Stepanov-like almost automorphic coefficients in a real separable Hilbert space.