Time-delayed feedback control of unstable periodic orbits near a subcritical Hopf bifurcation

We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of Fiedler et al. [PRL 98, 114101 (2007)], who demonstrated that such feedback control can stabilize the UPO associated with a two-dimensional subcritical Hopf normal form. Pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization, as well as knowledge of the period of the targeted UPO. We apply feedback in the directions tangent to the two-dimensional center manifold. We parameterize the feedback gain by a modulus and a phase angle, and give explicit formulae for choosing these two parameters given the period of the UPO in a neighborhood of the bifurcation point. We show, first heuristically, and then rigorously by a center manifold reduction for delay differential equations, that the stabilization mechanism involves a highly degenerate Hopf bifurcation problem that is induced by the time-delayed feedback. When the feedback gain modulus reaches a threshold for stabilization, both of the genericity assumptions associated with a two-dimensional Hopf bifurcation are violated: the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied, and the real part of the cubic coefficient of the normal form vanishes. Our analysis of this degenerate bifurcation problem reveals two qualitatively distinct cases when unfolded in a two-parameter plane. In each case, Pyragas-type feedback successfully stabilizes the branch of small-amplitude UPOs in a neighborhood of the original bifurcation point, provided that the phase angle satisfies a certain restriction.Comment: 35 pages, 19 figure

Transient increases in albumin and hyaluronan in bronchoalveolar lavage fluid after quitting smoking: possible signs of reparative mechanisms

AbstractInhalation of tobacco smoke results in an accumulation of cells in the lower respiratory tract. The inflammatory response in the alveoli and lung interstitium may also be reflected by increased bronchoalveolar lavage (BAL) fluid concentrations of extracellular matrix components. The present study investigated the influence of smoking on the BAL fluid concentrations of albumin (ALB), hyaluronan (HA) and fibronectin (FN). Lavage fluids from 18 smokers were analysed before and at 1, 3, 6, 9 and 15 months after smoking cessation. Never-smokers (n=112) served as a reference group. The total cell concentration and the concentrations of macrophages, lymphocytes, neutrophils and eosinophils were higher (P<0·001–0·01) in smokers' BAL fluid than in never-smokers', but the values returned to normal within 9 months of smoking cessation. The HA concentration was higher (P<0·001) in smokers' than in never-smokers' BAL fluid, but FN and ALB did not differ. Transient increases in the concentrations of ALB and HA (P<0·01 for both) was observed within 6 months of smoking cessation. These findings indicate a temporary heightened alveolar-capillary permeability and an increased production and/or degradation of HA, being enhanced following smoking cessation. The findings probably reflect an initiation of a reparative process

Human blood eosinophils produce and secrete interleukin 4

AbstractInterleukin 4 (Il-4) is an immunoregulatory cytokine which induces T-cell proliferation and differentiation into a Th2 phenotype, and is of particular importance for the induction of IgE synthesis. In the present study, the capability of human peripheral blood eosinophils from allergic and non-allergic donors to produce Il-4 was examined. Using reverse transcribed polymerase chain reaction (RT-PCR), it was shown that highly purified eosinophils from allergic patients express mRNA for Il-4. Resting eosinophils also gave specific immunoreactivity with anti-Il-4 antibodies, consistent with translation of Il-4 mRNA. Light and electron microscopic immunocytochemistry revealed that Il-4 was prestored in the eosinophilic granules. These results were confirmed by Il-4 specific ELISA which showed that Il-4 production could be upregulated in the eosinophils and released from the eosinophils following stimulation with the calcium ionophore A23187. These data indicate that eosinophils may be an important source of Il-4 at sites of allergic inflammation. Thus, eosinophils may act as immunomodulatory cells enhancing the allergic response through formation of Th2-cells and inducing the isotype switching to IgE in human B-cells