Dynamical behaviors of a prey-predator system with impulsive control

In this paper, we study dynamics of a prey-predator system under the impulsive control. Sufficient conditions of the existence and the stability of semi-trivial periodic solutions are obtained by using the analogue of the Poincaré criterion. It is shown that the positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation. A strategy of impulsive state feedback control is suggested to ensure the persistence of two species. Furthermore, a steady positive period-2 solution bifurcates from the positive periodic solution by the flip bifurcation, and the chaotic solution is generated via a cascade of flip bifurcations. Numerical simulations are also illustrated which agree well with our theoretical analysis.     

A mathematical model of the systemic circulatory system with logistically defined nervous system regulatory mechanisms

A mathematical model is developed that accurately describes the pressure, volume and flow dynamics of the systemic circulatory system over the full physiological range of human pressures and volumes. At the heart of this model are mathematical representations for the autonomic and central nervous system reflexes which maintain arterial pressure, cardiac output and cerebral blood flow. These representations involve functions in which a maximum effect and a minimum effect are smoothly connected by a logistic transition. A new approach to modelling the pressure – volume relationship in a vessel with smooth muscle contraction is also presented. To test the model, simulations of cardiac arrest and various haemorrhagic situations were conducted, and predicted results were compared with clinical observations. Near-perfect agreement was obtained between predicted and observed values of the mean circulatory filling pressure, cardiac output and arterial pressure decay in the face of significant haemorrhage, and the critical values delineating progressive from non-progressive hypovolaemic shock.     

A landing theorem for periodic dynamic rays for transcendental entire maps with bounded post-singular set

In this article, we present a landing theorem for periodic dynamic rays for transcendental entire maps which have bounded post-singular sets, by using standard hyperbolic geometry results.     

某型机进近段高精度相对姿态实时测量技术

某型机在飞行训练过程中，进近段的二维相对姿态数据对于该型机安全着陆有着至关重要的作用。基于无线网络电台的双向数据传输系统能够实时获取进近段飞机相对理想着陆点的水平、垂直相对位置数据。通过上行链路上传着陆点的姿态数据，下行链路实时下传动动差分后的差分数据,最后在中心控制站进行二次数据处理。该技术获得的进近段二维相对姿态精度达到厘米级，满足飞行训练的需求。同时结合飞机显控数据以及视景图，以多角化动态关联的方式将实时获取的姿态数据等呈现给指挥员，更好地辅助指挥员进行着陆指挥工作。     

Critically prime interval orders

We prove that a prime interval order, not necessarily finite, has no prime upper cover if and only if it has width two. On the other hand, we prove that every finite prime N-free order has at least one prime upper cover.     

基于层次分析的主成分分析法及其应用

在分析了传统的层次分析法和主成分分析法的优缺点的基础上,扬长避短的将两种方法结合在一起,讨论了基于层次分析的主成分分析法.与新兴的决策评估方法相比,例如直觉模糊层次分析法,基于层次分析的主成分分析法更具有简洁性和直观性.最后,将方法应用于登陆作战的目标选择,得到了与实战结果相同的结论,验证了方法的可行性.     

Simultaneous spectrophotometric flow-through measurements of pH, carbon dioxide fugacity, and total inorganic carbon in seawater

An autonomous multi-parameter flow-through CO₂ system has been developed to simultaneously measure surface seawater pH, carbon dioxide fugacity (fCO₂), and total dissolved inorganic carbon (DIC). All three measurements are based on spectrophotometric determinations of solution pH at multiple wavelengths using sulfonephthalein indicators. The pH optical cell is machined from a PEEK polymer rod bearing a bore-hole with an optical pathlength of ∼15 cm. The fCO₂ optical cell consists of Teflon AF 2400 (DuPont) capillary tubing sealed within the bore-hole of a PEEK rod. This Teflon AF tubing is filled with a standard indicator solution with a fixed total alkalinity, and forms a liquid core waveguide (LCW). The LCW functions as both a long pathlength (∼15 cm) optical cell and a membrane that equilibrates the internal standard solution with external seawater. fCO₂ is then determined by measuring the pH of the internal solution. DIC is measured by determining the pH of standard internal solutions in equilibrium with seawater that has been acidified to convert all forms of DIC to CO₂. The system runs repetitive measurement cycles with a sampling frequency of ∼7 samples (21 measurements) per hour. The system was used for underway measurements of sea surface pH, fCO₂, and DIC during the CLIVAR/CO₂ A16S cruise in the South Atlantic Ocean in 2005. The field precisions were evaluated to be 0.0008 units for pH, 0.9 μatm for fCO₂, and 2.4 μmol kg⁻¹ for DIC. These field precisions are close to those obtained in the laboratory. Direct comparison of our measurements and measurements obtained using established standard methods revealed that the system achieved field agreements of 0.0012 ± 0.0042 units for pH, 1.0 ± 2.5 μatm for fCO₂, and 2.2 ± 6.0 μmol kg⁻¹ for DIC. This system integrates spectrophotometric measurements of multiple CO₂ parameters into a single package suitable for observations of both seawater and freshwater.     

Integral invariants for non-barotropic flows in a four dimensional space time manifold

Properties of non-barotropic flows are described using Lie derivatives of differential forms in a Euclidean four dimensional space-time manifold. Vanishing of the Lie derivative implies that the corresponding physical quantity remains invariant along the integral curves of the flow. Integral invariants of non-barotropic perfect and viscous flows are studied using the concepts of relative and absolute invariance of forms. The four dimensional expressions for the rate of change of the generalized circulation, generalized vorticity flux, generalized helicity and generalized parity in the case of ideal and viscous non-barotropic flows are thereby obtained.     

A semi-algebraic approach for asymptotic stability analysis

This paper deals with the problem of computing Lyapunov functions for asymptotic stability analysis of autonomous polynomial systems of differential equations. We propose a new semi-algebraic approach by making advantage of the local property of the Lyapunov function as well as its derivative. This is done by first constructing a semi-algebraic system and then solving this semi-algebraic system in an adaptive way. Experiment results show that our semi-algebraic approach is more efficient in practice, especially for low-order systems.