Mackey-Glass type delay differential equations near the boundary of absolute stability

For equations $x'(t) = -x(t) + \zeta f(x(t-h)), x \in \R, f'(0)= -1, \zeta > 0,$ with $C^3$-nonlinearity $f$ which has negative Schwarzian derivative and satisfies $xf(x) < 0$ for $x\not=0$, we prove convergence of all solutions to zero when both $\zeta -1 >0$ and $h(\zeta-1)^{1/8}$ are less than some constant (independent on $h,\zeta$). This result gives additional insight to the conjecture about the equivalence between local and global asymptotical stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of Mathematical Analysis and Application

Global stability in a regulated logistic growth model

Trofimchuk, S. Instituto de Matemática y Física, Universidad de Talca, Casilla 747, Talca, Chile.We investigate global stability of the regulated logistic growth model (RLC) n'(t) = rn(t)(1-n(t-h)/K-cu(t)), u'(t) = -au(t)+bn(t-h). It was proposed by Gopalsamy and Weng [1, 2] and studied recently in [4, 5, 6, 9]. Compared with the previous results, our stability condition is of different kind and has the asymptotical form. Namely, we prove that for the fixed parameters K and mu = bcK/a (which determine the levels of steady states in the delayed logistic equation n'(t) rn(t)(1 - n(t - h)/K) and in RLG) and for every hr < root 2 the regulated logistic growth model is globally stable if we take the dissipation parameter a sufficiently large. On the other hand, studying the local stability of the positive steady state, we observe the improvement of stability for the small values of a: in this case, the inequality rh < pi(1 + mu)/2 guaranties such a stabilit

Yorke and Wright 3/2-stability theorems from a unified point of view

We consider a family of scalar delay differential equations $x'(t)=f(t,x_t)$, with a nonlinearity $f$ satisfying a negative feedback condition combined with a boundedness condition. We present a global stability criterion for this family, which in particular unifies the celebrated 3/2-conditions given for the Yorke and the Wright type equations. We illustrate our results with some applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS, devoted to the fourth international conference on Dynamical Systems and Differential Equations, held at UNC at Wilmington, May 2002. Minor changes from the previous versio

Pushed traveling fronts in monostable equations with monotone delayed reaction

We study the existence and uniqueness of wavefronts to the scalar reaction-diffusion equations $u_{t}(t,x) = \Delta u(t,x) - u(t,x) + g(u(t-h,x)),$ with monotone delayed reaction term $g: \R_+ \to \R_+$ and $h >0$. We are mostly interested in the situation when the graph of $g$ is not dominated by its tangent line at zero, i.e. when the condition $g(x) \leq g'(0)x,$ $x \geq 0$, is not satisfied. It is well known that, in such a case, a special type of rapidly decreasing wavefronts (pushed fronts) can appear in non-delayed equations (i.e. with $h=0$). One of our main goals here is to establish a similar result for $h>0$. We prove the existence of the minimal speed of propagation, the uniqueness of wavefronts (up to a translation) and describe their asymptotics at $-\infty$. We also present a new uniqueness result for a class of nonlocal lattice equations.Comment: 17 pages, submitte

The influence of diverse optical wavelengths on growth rate of Chlorella Vulgaris microalgae

The effect of different optical wavelengths on growth and development of microalgae had been examined repeatedly. Many articles had been published over the subject, although the results of these investigations were frequently controversial. Depending on the number of days spent on cultivation process, yield gain could be both significant and barely noticeable. Also, irradiation intensity plays vital part in microalgae functioning

The influence of PAR irradiance on yield growth of Chlorella microalgae

The experiment indicated the influence of different PAR irradiance conditions on biomass growth of Chlorella vulgaris Beijer stock culture. The absorption spectrum of suspension was evaluated with spectrophotometer SF-256 UVI LOMO Photonika. In this work, effects of LED lamps with various radiant powers on yield gain were compared by analyzing the relation between cells concentration increase and time. It was concluded, that light is the most important factor influencing growth and cells development, as well as nutrient solution, temperature and carbon dioxide provision

Особенности течения гриппа, вызванного новым вирусом А / H1N1 / CA / 2009, у больных в амбулаторной практике

Summary. Emergence of a new influenza virus А / H1N1 / CA / 2009 (IA2009) in October–December, 2009, in Russia required to investigate clinical features of the infection and effectiveness of treatment in ambulatory practice. Information from outpatient medical cards of 44 patients seeking for medical aid because of acute respiratory viral infection (ARVI) during pandemic 2009 was analyzed. All patients were examined for the presence of influenza А / H1N1 / CA / 2009 virus RNA, seasonal influenza virus RNA and influenza B virus RNA in nasopharyngeal swabs using polymerase chain reaction (PCR). According to the PCR results, patients were identified as having influenza А / H1N1 (n = 21) or other ARVI (n = 23). Signs and symptoms, complete blood count test, urine test, and chest X-ray were analyzed. Retrospective analysis found that 76.2 % of influenza А / H1N1 patients had acute respiratory diseases during previous 12 months and 19.0 % of them were healthcare workers. Leading symptoms and signs in patients with influenza А / H1N1 were cough, headache, weakness, myalgia, fever, obstruction of upper and lower airways. Mild course of disease was observed only in 23.8 % of the cases with recovery during 10 days. Complications were found in 28.6 % of the patients, 14.3 % of them were hospitalized. The most frequent changes in complete blood count tests were accelerated erythrocyte sedimentation rate, neutropenia / leucopenia, lymphocytosis, monocytosis, anisocytosis, thrombocyte aggregation. In 31.3 % cases, changes in white cell count remained after clinical recovery and resolving all respiratory symptoms. Administration of antiviral antibiotic Ingavirin in patients with influenza А / H1N1 started in the first 2 days of the disease was more effective compared with immunomodulating drug Arbidol.Резюме. Эпидемическая циркуляция нового вируса гриппа А / H1N1 / CA / 2009 в России в октябре–декабре 2009 г. потребовала изучения особенностей течения болезни и эффективности лечения больных гриппом в условиях поликлиники. Был проведен анализ данных 44 амбулаторных карт больных, обратившихся в поликлинику в период эпидемического подъема заболеваемости по поводу острой респираторной вирусной инфекции. Все больные были обследованы на наличие РНК вируса гриппа А / H1N1 / CA / 2009, сезонного гриппа А и гриппа В в мазках со слизистой носоглотки методом полимеразной цепной реакции (ПЦР) в режиме реального времени. По результату ПЦР были выделены больные гриппом А / H1N1 (n = 21) и ОРВИ (n = 23). Анализировались частота субъективных и объективных признаков болезни, показатели анализа крови, общего анализа мочи, рентгенографии грудной клетки, тактика ведения больных. Оценивались тяжесть течения и частота осложнений, данные об острых заболеваниях в последние 12 мес., а так же хронических болезнях. Ретроспективный анализ данных амбулаторных карт показал, что 76,2 % больных гриппом в течение 12 мес. до эпидемии перенесли острое заболевание органов дыхания. 19 % больных гриппом были медицинскими работниками. В течение 3 дней от начала заболевания обратились за медицинской помощью 14,3 % пациентов; ведущими субъективными симптомами были кашель, головная боль, слабость, боль в мышцах. В клинической картине для гриппа были характерны повышенная температура (100 % случаев), поражение верхних и нижних отделов дыхательных путей с признаками обструкции. В 76,2 % случаев отмечалось среднетяжелое и тяжелое течение болезни. Осложнения имели 28,6 % пациентов, в 14,3 % случаев им была необходима госпитализация. Вирус гриппа обнаруживался методом ПЦР в слизи из носоглотки до 11 дней болезни. Изменения в анализе крови при гриппе были обнаружены в 100 % случаев. Наиболее частыми были ускорение скорости оседания эритроцитов, нейтропения / лейкопения, лимфоцитоз, моноцитоз, анизоцитоз, агрегация тромбоцитов, которые сохранялись в 31,3 % случаев и при отсутствии клинических симптомов. Противовирусная терапия в первые 2 сут. от начала гриппа и ОРВИ сокращала продолжительность болезни. Назначение препарата ингавирин при гриппе было более эффективно, чем препарата арбидол