Numerical bifurcation analysis of delay differential equations

AbstractNumerical methods for the bifurcation analysis of delay differential equations (DDEs) have only recently received much attention, partially because the theory of DDEs (smoothness, boundedness, stability of solutions) is more complicated and less established than the corresponding theory of ordinary differential equations. As a consequence, no established software packages exist at present for the bifurcation analysis of DDEs. We outline existing numerical methods for the computation and stability analysis of steady-state solutions and periodic solutions of systems of DDEs with several constant delays

Cloning and characterization of the lectin cDNA clones from onion, shallot and leek

Characterization of the lectins from onion ( Allium cepa ), shallot ( A. ascalonicum ) and leek ( A. porrum ) has shown that these lectins differ from previously isolated Alliaceae lectins not only in their molecular structure but also in their ability to inhibit retrovirus infection of target cells.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/43434/1/11103_2004_Article_BF00029011.pd

Computation, continuation and bifurcation analysis of periodic solutions of delay differential equations

this paper we present a new numerical method for the e#cient computation of periodic solutions of DDEs and the determination of their stability. This approach exploits the fact that zero is a cluster point for the Floquet multipliers [Hale, 1977]. Usually only a few Floquet multipliers have large modulus. Therefore we can use the ideas behind the Newton--Picard method developed for the computation of periodic solutions of dissipative systems of PDEs [Roose et al., 1995; Lust et al., 1996]. This algorithm can compute branches of periodic solutions and at little extra cost also the dominant, stability-determining Floquet multipliers. We now extend this method to compute periodic solutions of a DDE or a system of DDEs. We avoid an approximation of a DDE by a high order system of ODEs, which has been widespread in the mathematical and engineering literature [Bank & Burns, 1978]. The disadvantage of this approach is that an extremely large system of ODEs is necessary to obtain a good approximation for a periodic solution of a DDE, which leads to a very expensive method. In Sec. 2 we formulate the periodicity problem for DDEs in an infinite dimensional space and suggest a finite dimensional approximation of this problem through the discretization of an initial function on the delay interval. Using the discrete version of the Poincare operator, we construct a nonlinear system which allows to compute the segment of the periodic solution on the delay interval and the value of its period. This leads to a single-shooting approach which is the starting point of the Newton--Picard algorithm. In Sec. 3 we briefly describe the main ideas of the Newton--Picard algorithm and consider its application to DDEs. Results of numerical experiments are presented in Sec. 4. In Sec. 5 we summariz..

Continuous pole placement method for delay equations

In this paper, we describe a stabilization method for linear time-delay systems which extends the classical pole placement method for ordinary differential equations. Unlike methods based on finite spectrum assignment, our method does not render the closed loop system, finite dimensional but consists of controlling the rightmost eigenvalues. Because these are moved to the left half plane in a (quasi-)continuous way, we refer to our method as continuous pole placement. We explain the method by means of the stabilization of a linear finite dimensional system in the presence of an input delay and illustrate its applicability to more general stabilization problems. © 2002 Elsevier Science Ltd. All rights reserved.status: publishe

A Fluorescence Lifetime Study of Virginiamycin-s Using Multifrequency Phase Fluorometry

Using multifrequency phase fluorometry, fluorescence lifetimes have been assigned to the different protolytic forms of the antibiotic virginiamycin S. These lifetimes are 0.476 +/-0.005 ns for the uncharged form, 1.28 +/- 0.2 and 7.4 +/- 0.2 ns for the zwitterionic form, 1.19 +/- 0.01 ns for the negatively charged form, and 1.9 +/- 0.1 ns for the double negatively charged form. The assignments are based on lifetime measurements as a function of pH, volume percent ethanol, and excitation wavelength. Excited-state proton transfer is taken into account. It is complete at pH values lower than 1, and no fluorescence of the fully protonated charged form is observed. At pH 8, an excited-state pK* increase is calculated, but proton association is too slow to cause excited-state proton transfer. The addition of divalent cations, at pH 9.4, increases the lifetime of the negatively charged form to a value dependent upon the specific nature of the cation (7.58 +/- 0.06 ns for Mg2+, 6.54 +/- 0.02 ns for Ca2+, and 3.74 +/- 0.05 ns for Ba2+). Monovalent cations do not influence the lifetimes, indicating that their binding to the macrocycle does not influence the fluorescent moiety, The model compound 3-hydroxypicolinamide shows an analogous behavior, but the retrieved lifetime can differ significantly