Delay driven Hopf bifurcation and chaos in a diffusive toxin producing phytoplankton‐zooplankton model

This paper deals with a diffusive toxin producing phytoplankton‐zooplankton model with maturation delay. By analyzing eigenvalues of the characteristic equation associated with delay parameter, the stability of the positive equilibrium and the existence of Hopf bifurcation are studied. Explicit results are derived for the properties of bifurcating periodic solutions by means of the normal form theory and the center manifold reduction for partial functional differential equations. Numerical simulations not only agree with the theoretical analysis but also exhibit the complex behaviors such as the period‐3, 5, 6, 7, 8, 11, and 12 solutions, cascade of period‐doubling bifurcation in period‐2, 4, quasi‐periodic solutions, and chaos. The key observation is that time delay may control harmful algae blooms (HABs). Moreover, numerical simulations show that the chaotic states induced by the period‐doubling bifurcation are purely temporal, which is stationary in space and oscillatory in time. The investigations may provide some new insights on harmful phytoplankton blooms.     

Ignition delay times of methane and hydrogen highly diluted in carbon dioxide at high pressures up to 300 atm

The need for more efficient power cycles has attracted interest in super-critical CO₂ (sCO₂) cycles. However, the effects of high CO₂ dilution on auto-ignition at extremely high pressures has not been studied in depth. As part of the effort to understand oxy-fuel combustion with massive CO₂ dilution, we have measured shock tube ignition delay times (IDT) for methane/O₂/CO₂ mixtures and hydrogen/O₂/CO₂ mixtures using sidewall pressure and OH* emission near 306?nm. Ignition delay time was measured in two different facilities behind reflected shock waves over a range of temperatures, 1045–1578?K, in different pressures and mixture regimes, i.e., CH₄/O₂/CO₂ mixtures at 27–286 atm and H₂/O₂/CO₂ mixtures at 37–311 atm. The measured data were compared with the predictions of two recent kinetics models. Fair agreement was found between model and experiment over most of the operating conditions studied. For those conditions where kinetic models fail, the current ignition delay time measurements provide useful target data for development and validation of the mechanisms.     

Periodic Solutions of Third-order Differential Equations with Finite Delay in Vector-valued Functional Spaces

In this paper, we study the well-posedness of the third-order differential equation with finite delay(P_3): αu'"(t) + u"(t) = Au(t) + Bu'(t) + Fut +f(t)(t ∈ T := [0,2π]) with periodic boundary conditions u(0) = u(2π), u'(0) = u"(2π),u"(0)=u"(2π) in periodic Lebesgue-Bochner spaces Lp(T;X) and periodic Besov spaces B_(p,q)~s(T;X), where A and B are closed linear operators on a Banach space X satisfying D(A) ∩ D(B) ≠ {0}, α≠ 0 is a fixed constant and F is a bounded linear operator from Lp([-2π, 0]; X)(resp. Bp,qs([-2π, 0]; X)) into X, ut is given by ut(s) = u(t + s) when s ∈ [-2π,0]. Necessary and sufficient conditions for the Lp-well-posedness(resp. B_(p,q)~s-well-posedness)of(P_3) are given in the above two function spaces. We also give concrete examples that our abstract results may be applied.     

Robust stabilization of a class of state-dependent jump linear systems

In this article, we consider a continuous-time state-dependent jump linear system (SDJLS), a kind of stochastic hybrid system, with the presence of uncertainties in system parameters. In SDJLS, we consider that the transition rates of the underlying random jump process depend on the state variable. In particular, we assume the transition rates to have different values across suitably defined sets to which the state of the system belongs, and address a problem of robust stability and stabilization analysis. We obtain sufficient conditions for robust stability and state-feedback stabilization in terms of linear matrix inequalities (LMIs). We validate the obtained sufficient robust stability and stabilization conditions with numerical examples.     

具有固定时滞的经济周期模型的动态分析

在经济活动中,投资行为和资本存量存在一定的时滞效应,这会影响经济周期模型的动态行为,进而使得投资政策对经济的稳定调整复杂化.考虑到资本存量的预期时间以及投资时滞对经济活动的影响,采用Hopf分岔理论,研究具有固定时滞的经济周期模型的均衡点的稳定性以及形成经济周期的条件.研究发现,投资过程中的投资时滞,以及投资决策中对于资本存量的预测时间构成经济周期产生的诱因;同时可通过政府投资政策调整达到预期均衡目标,这对保持经济周期稳定及经济政策制定有一定的指导作用.     

一类非线性时滞网络控制系统的无源性分析

本文研究了一类非线性时滞网络控制系统的无源性问题.利用Lyapunov稳定性理论,结合线性矩阵不等式(LMI)技术,通过构造Lyapunov-Krasovskii泛函,在考虑两种不同时滞的情况下,获得了系统满足无源性的充分条件,最后通过仿真算例验证了结论的正确性和方法的有效性.     

Spectrochemical analysis using LIBS and ICP-OES techniques of herbal medicine (Tinnevelly Senna leaves) and its anti-cancerous/antibacterial applications

Tinnevelly senna leaves are being applied to cure many diseases especially in developing countries and sub-Saharan region due to many bioactive compounds such as sennosides, phenols, and flavonoids. The conventional methods to isolate and analyze plant extracts biomolecules are not very effective as well cost effective as they require hazardous chemical solvents and reagents, which are time-consuming processes. The major objective of the present study is to investigate the feasibility of the Laser induced breakdown spectroscopy (LIBS) technique for rapid, eco-friendly, and multi-elemental analysis of Senna leaves extracts and study their antibacterial and anticancer potentials. The elegant LIBS technique was applied as a qualitative and quantitative method for Senna leaves sample’s elemental analysis and their biological activities were measured by evaluating anti-cancer and anti-bacterial analysis. The quantitative analysis of Senna leaves extracts was done using the calibration-free laser-induced breakdown spectroscopy (CF-LIBS) algorithm showing their appreciable content of several nutrient elements, and the obtained results were in close conformity with these achieved by using the standard analytical ICP OES technique. We studied the bactericidal efficacy of the Senna leaves extract against Staphylococcus aureus (S. aureus) by AWD assays and morphogenesis by scanning electron microscopy (SEM) and the anticancer activity was also investigated where different concentrations of Senna leaves extract were tested on cancer cells (HCT-116 and HeLa) and normal cells (HEK-293) using the cell metabolic activity MTT assay and Propidium iodide (PI) staining. We have also calculated the inhibitory concentration (IC50) value for the various extracts concentrations (25 µg/ml, 50 µg/ml, 100 µg/ml, 150 µg/ml, 200 µg/ml, and 225 µg/ml). We have found that IC₅₀ value for HCT-116 cells were 13.5 µg/ml, 17.5 µg/ml, 21.5 µg/ml, 22.5 µg/ml, 26 µg/ml and 33.5 µg/ml and for HeLa cells 15.25 µg/ml, 21.25 µg/ml, 23.5 µg/ml, 262.5 µg/ml, 36.25 µg/ml, and 39.50 µg/ml. The bactericidal efficacy of the Senna leaves extract showed significant inhibition against Gram-positive bacterium. Both MTT and PI analysis showed that Senna leaves extract induced profound inhibition on HCT-116 growth and proliferation. Additionally, Senna leaves extract did not exert an inhibitory influence on normal (HEK-293), which is non-cancerous cells. We suggest that the extract specifically targets the cancerous cells, which could be highly beneficial for the development of future safe anticancer and antibacterial drugs using these extracts.     

Functional Differential Equations With Delay and Random Effects

The authors study the existence of mild solutions to a functional differential equation with delay and random effects. They use a random fixed point theorem with a stochastic domain. An example is included to illustrate their results.     

8×8APD阵列激光三维成像接收机研制

为了实现对目标的无扫描阵列激光三维成像并研究系统参数对三维成像距离分辨率的影响,研制了8×8 pixel激光三维成像接收机。接收机采用线性模式APD阵列,设计了模拟信号放大、阈值处理将回波光信号转换为数字信号后,利用FPGA设计实现64通道高精度阵列计时系统,实现了对目标的无扫描实时三维成像功能。首先对设计完成的三维成像接收机组成及成像原理进行了介绍,对三维成像接收机中APD探测器阵列信号的模拟处理和数字处理流程和实现方式进行了说明。随后分别对三维成像的核心FPGA计时系统及探测器整体进行了电子学测试和实验测试。测试结果表明,FPGA计时子系统的时间分辨率优于140 ps,三维成像系统整体距离分辨率在0.2 m左右。最后对分辨率的误差进行了分析,结果表明,激光回波强度波动是影响此接收机距离分辨率的最主要因素。