Stochastic delay foraging arena predator–prey system with Markov switching

Abstract

In this paper, we introduce white noise, telegraph noise and time delay to the two-dimensional foraging arena population system describing the prey and predator abundance. The aim is to find out how the interactions between white noise, telegraph noise and time delay affect the dynamics of the population system. Firstly, the existence of a global positive solution is verified. Then the long-time properties including the stochastically ultimate boundedness, extinction and some other asymptotic pathwise estimation of this population system are studied. Finally, the main results are illustrated by two examples.     

Blow-up behavior of Hammerstein-type delay Volterra integral equations

We consider the blow-up behavior of Hammerstein-type delay Volterra integral equations (DVIEs). Two types of delays, i.e., vanishing delay (pantograph delay) and non-vanishing delay (constant delay), are considered. With the same assumptions of Volterra integral equations (VIEs), in a similar technology to VIEs, the blow-up conditions of the two types of DVIEs are given. The blow-up behaviors of DVIEs with non-vanishing delay vary with different initial functions and the length of the lag, while DVIEs with pantograph delay own the same blow-up behavior of VIEs. Some examples and applications to delay differential equations illustrate this influence.     

On fractional integro-differential inclusions with state-dependent delay in Banach spaces

In this article we investigate the existence of solutions on a compact interval for the fractional integro-differential inclusions with state-dependent delay in Banach spaces when the delay is infinite. We consider the cases when the multivalued nonlinear term takes convex values as well as nonconvex values.     

Finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay via periodically intermittent control

In this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results.     

Existence and attractivity of time periodic solutions for Nicholson's blowflies model with nonlinear diffusion

This paper is concerned with the existence and attractivity of time periodic solutions for one‐dimensional Nicholson's blowflies model with nonlinear diffusion. By constructing some suitable Lyapunov functionals and combining with Leray–Schauder fixed point theorem, we establish the existence of nonnegative time periodic solutions. Using the method of upper and lower solutions and its associated monotone iterations, we obtain the existence of the attractor for this model. Copyright © 2013 John Wiley & Sons, Ltd.     

Multiple resonances with time delays in scale-free networks of Hodgkin-Huxley neurons subjected to non-Gaussian noise

The spiking behavior with varying time delay in scale-free networks of Hodgkin-Huxley neurons with non-Gaussian noise has been studied,and the effect of non-Gaussian noise on the delay-induced spiking behavior is discussed. It was found that multiple spatio-temporal resonances occur when the delay lengths are integer multiples of the spiking periods,and the resonances may be strengthened when the non-Gaussian noise is appropriate. This result shows that time delays can optimize the spiking temporal regulari...     

煤油裂解产物/空气与煤油/空气在宽温度范围内点火延迟的对比研究

Kerosene is an ideal endothermic hydrocarbon. Its pyrolysis plays a significant role in the thermal protection for high-speed aircraft. Before it reacts, kerosene experiences thermal decomposition in the heat exchanger and produces cracked products. Thus, to use cracked kerosene instead of pure kerosene, knowledge of their ignition properties is needed. In this study, ignition delay times of cracked kerosene/air and kerosene/air were measured in a heated shock tube at temperatures of 657–1333 K, an equivalence ratio of 1.0, and pressures of 1.01 × 10⁵–10.10 × 10⁵ Pa. Ignition delay time was defined as the time interval between the arrival of the reflected shock and the occurrence of the steepest rise of excited-state CH species (CH*) emission at the sidewall measurement location. Pure helium was used as the driver gas for high-temperature measurements in which test times needed to be shorter than 1.5 ms, and tailored mixtures of He/Ar were used when test times could reach up to 15 ms. Arrhenius-type formulas for the relationship between ignition delay time and ignition conditions (temperature and pressure) were obtained by correlating the measured high-temperature data of both fuels. The results reveal that the ignition delay times of both fuels are close, and an increase in the pressure or temperature causes a decrease in the ignition delay time in the high-temperature region (> 1000 K). Both fuels exhibit similar high-temperature ignition delay properties, because they have close pressure exponents (cracked kerosene: τ_ign∝P^-0.85; kerosene:τ_ign∝P^-0.83) and global activation energies (cracked kerosene: E_a = 143.37 kJ·mol^-1; kerosene: E_a = 144.29 kJ·mol^-1). However, in the low-temperature region (< 1000 K), ignition delay characteristics are quite different. For cracked kerosene/air, while the decrease in the temperature still results in an increase in the ignition delay time, the negative temperature coefficient (NTC) of ignition delay does not occur, and the low-temperature ignition data still can be correlated by an Arrhenius-type formula with a much smaller global activation energy compared to that at high temperatures. However, for kerosene/air, this NTC phenomenon was observed, and the Arrhenius-type formula fails to correlate its low-temperature ignition data. At temperatures ranging from 830 to 1000 K, the cracked kerosene ignites faster than the kerosene; at temperatures below 830 K, kerosene ignition delay times become much shorter than those of cracked kerosene. Surrogates for cracked kerosene and kerosene are proposed based on the H/C ratio and average molecular weight in order to simulate ignition delay times for cracked kerosene/air and kerosene/air. The simulation results are in fairly good agreement with current experimental data for the two fuels at high temperatures (> 1000 K). However, in the low-temperature NTC region, the results are in very good agreement with kerosene ignition delay data but disagree with cracked kerosene ignition delay data. The comparison between experimental data and model predictions indicates that refinement of the reaction mechanisms for cracked kerosene and kerosene is needed. These test results are helpful to understand ignition properties of cracked kerosene in developing regenerative cooling technology for high-speed aircraft.     

A theory of adsorption kinetics with time delay and its application to overshoot and oscillation in the surface tension of gelatin solution

A theory of adsorption kinetics with time delay [Ohshima et al. (1992) Colloid Polym. Sci. 270:707] is developed and applied to the surface tension of a polymer solution. It is found that the general appearance of the overshoot and oscillation in the time course of the surface tension of aqueous gelatin solution observed by Sato and Ueberreiter [(1979) Makromol. Chem. 180:829, 1107; (1979) Polym. Prepr. Am. Chem. Soc. Div. Polym. Chem. 20:907) can be explained by the present theory.     

正十一烷/空气在宽温度范围下着火延迟的激波管研究

在加热激波管上测量了气相正十一烷/空气混合物的着火延迟时间,着火温度为宽温度范围731-1399 K,着火压力在2.02 × 10⁵和10.10 × 10⁵ Pa附近,化学计量比分别为0.5、1.0和2.0。通过监测管侧壁观测点处的反射激波压力和OH^*发射光测出着火延迟时间。实验结果显示：在910 K以上,着火延迟时间随着火温度的降低而变长,从910到780 K,着火延迟时间随着火温度的降低而变短（显示出了负温度系数效应）,在780 K以下,着火延迟时间随着火温度的降低再次变长。在所研究的压力下,着火压力的增加使着火时间变短。化学计量比对着火延迟的影响在着火压力为2.02 × 10⁵和10.10 × 10⁵ Pa时是不同的,与在高温区相比,着火延迟在低温区对化学计量比非常敏感。在整个温度范围内,当前实验结果和LLNL（LawrenceLivermore National Laboratory）机理的预测值表现出了很好的一致性。现在的正十一烷/空气的着火数据和先前实验测量的正庚烷/空气、正癸烷/空气和正十二烷/空气的着火延迟时间相比较显示了着火延迟时间随着直链烷碳原子数的增加而减小。敏感度分析显示,高、低温条件下影响正十一烷着火延迟过程的反应是显著不同的。在高温条件下起最大促进作用的反应是H + O₂=O+OH,然而在低温条件下,起最大促进作用的反应是过氧十一烷基（C₁₁H₂₃O₂）的异构化反应。本文研究首次提供了正十一烷/空气的激波管着火延迟时间。     

Construction of a Chemical Kinetic Model of Five-Component Gasoline Surrogates under Lean Conditions

The requirements for improving the efficiency of internal combustion engines and reducing emissions have promoted the development of new combustion technologies under extreme operating conditions (e.g., lean combustion), and the ignition and combustion characteristics of fuels are increasingly becoming important. A chemical kinetic reduced mechanism consisting of 115 species and 414 elementary reactions is developed for the prediction of ignition and combustion behaviors of gasoline surrogate fuels composed of five components, namely, isooctane, n-heptane, toluene, diisobutylene, and cyclohexane (CHX). The CHX sub-mechanism is obtained by simplifying the JetSurF2.0 mechanism using direct relationship graph error propagating, rate of production analysis, and temperature sensitivity analysis and CHX is mainly consumed through ring-opening reactions, continuous dehydrogenation, and oxygenation reactions. In addition, kinetic parameter corrections were made for key reactions R14 and R391 based on the accuracy of the ignition delay time and laminar flame velocity predictions. Under a wide range of conditions, the mechanism’s ignition delay time, laminar flame speed, and the experimental and calculated results of multi-component gasoline surrogate fuel and real gasoline are compared. The proposed mechanism can accurately reproduce the combustion and oxidation of each component of the gasoline-surrogate fuel mixture and real gasoline.