We consider a known model that describes formation of mussel beds on soft sediments. The model consists of nonlinearly coupled pdes that capture evolution of mussel biomass on the sediment and algae in the water layer overlying the mussel bed. The system accounts for the diffusive spread of mussel, while the diffusion of algae is neglected and at the same time the tidal flow of the water is con...

Considering a continuous time LTI system, with impulse response hc t , the uniformly spaced samples hc nT can be identified by using an impulse train input with an arbitrarily small rate 1/NT and sampling the system output with an arbitrarily small rate 1/MT, provided M and N to be coprime for any chosen time spacing T. It is shown that different LTI filters can be identified using the sparse c...

Abstract: In this paper, the transmission zero at s radius and the minimum phase radius of a linear time-invariant (LTI) system are introduced. The former radius gives a measure of how “near” a LTI system is from having a transmission zero at a specified point s ∈ C in the complex plane, and the latter radius measures how “near” a minimum phase system is to a nonminimum phase system. Formulas f...

in the present paper the linear oscillator in r3 with z =constanthas been considered. the aim is to determine the necessary conditions forthe persistence of periodic solutions under discontinuous perturbations. a newapproach based on a computational method has been used. at the end weapply our method on an example.

Embedded solitons are solitary waves residing inside the continuous spectrum of a wave system. They have been discovered in a wide array of physical situations recently. In this article, we present the first comprehensive theory on the dynamics of embedded solitons and nonlocal solitary waves in the framework of the perturbed fifth-order Korteweg–de Vries (KdV) hierarchy equation. Our method is...

This paper investigates the stabilization problem for interconnected linear time-invariant (LTI) time-delay system by means of a linear time-invariant output feedback decentralized controller. The delays are assumed to be commensurate and can appear in the states, inputs, and outputs of the system. First, the canonical forms for time-delay systems with commensurate delays are introduced and cen...

In this article we deal with singularly perturbed Filippov systems Zε:

This article presents a fairly complete account on various topological and metrical aspects of feedback stabilization for single-input single-output (SISO) continuous discrete time linear time-invariant (LTI) systems. In particular, we prove that the set stabilizing output gains SISO system with n states have at most [n/2] connected components. Furthermore, our analysis yields an algorithm dete...

On the conditioning of an upwind nite-diierence approximation of a convection-diiusion boundary value problem on an adaptive grid. We derive condition number estimates for the standard rst-order upwind numerical discretisation of a model convection-diiusion boundary value problem on a non-uniform grid. The grid is suggested by the equidistribution of a power of the solution gradient. It is show...