一类求解奇异延迟微分方程的两步连续Runge-Kutta方法的收敛性

本文给出了一类求解延迟落在当前积分步内延迟微分方程的两步连续Runge-Kutta方法。在一定条件下我们证明了方法收敛性,数值试验表明方法是有效的。     

线性时滞系统实用稳定性的一个简明判据

利用比较的方法，获得了线性时滞系统实用稳定性的一个简单判定定理．     

Exponential boundedness of solutions for impulsive delay differential equations

For an impulsive delay differential equation

exponent estimates of solutions have been obtained.     

Determination of the optimal initial function and the parameters for nonlinear time-delay systems

This paper deals with dynamic systems described by nonlinear differential-difference equations of retarded type. The problem considered is to determine the initial function and certain system parameters which minimize a given cost functional. A computational method is presented and some convergence results are given. Numerical examples of linear and nonlinear systems are also included.     

Hopf bifurcation of a tumor immune model with time delay

In this paper, a tumor immune model with time delay is studied. First, the stability of nonnegative equilibria is analyzed. Then the time delay τ is selected as a bifurcation parameter and the existence of Hopf bifurcation is proved. Finally, by using the canonical method and the central manifold theory, the criteria for judging the direction and stability of Hopf bifurcation are given.     

Set controllability of Markov jump switching Boolean control networks and its applications

In this article, a novel method is proposed for investigating the set controllability of Markov jump switching Boolean control networks (MJSBCNs). Specifically, the switching signal is described as a discrete-time homogeneous Markov chain. By resorting to the expectation and switching indicator function, an expectation system is constructed. Based on the expectation system, a novel verifiable condition is established for solving the set reachability of MJSBCNs. With the newly obtained results on set reachability, a necessary and sufficient condition is further derived for the set controllability of MJSBCNs. The obtained results are applied to Boolean control networks with Markov jump time delays. Examples are demonstrated to justify the theoretical results.     

Limit cycles of a class of Liénard systems derived from state-dependent impulses

Discontinuous phenomena, in which objects may behave continuously and sometimes discretely are not only found in nature and under laboratory conditions but also in simple, familiar contexts. For example, this phenomenon is skillfully incorporated into the internal structure of mechanical wristwatches. Unless an extremely small amount of state-dependent impulse is applied intermittently, the reciprocating rotational movement of the balance and hairspring, which is the heart of the mechanical wristwatch, cannot be maintained. The small amount of state-dependent impulse, which is often overlooked, can make a significant difference; however, very few studies have examined this subject. This study assumes the underlying cause of discontinuous behaviors as impulses generated when an object reaches a particular state, assuming that the continuous behavior follows the Liénard system, which is widely studied in the field of electrical circuits. The main theorem provides the conditions under which the effect of the impulses causes a stable limit cycle in the Liénard system, even if no limit cycle exists when there are no impulses. The Poincaré–Bendixson theorem for discontinuous dynamical systems and phase plane analysis are used to prove the main theorem. Several examples and their simulations are provided to illustrate the main theorem.     

Surface recombination in breakdown time delay experiments: Effect of different cathode materials

The late afterglow in nitrogen with iron electrode is studied by the breakdown time delay method, i.e., by measuring the breakdown time delay t_d as a function of the afterglow time . It is proposed that the cause of the secondary electrons initiating the breakdown is the energy of the surface recombination of nitrogen atoms on the iron electrode. The gas-phase and macrokinetic diffusive models are used to describe the experimental breakdown time delay data. By fitting the theoretical curve to the experimental data: (1) it has been confirmed that the recombination on the molybdenum glass is of the second order and the value of the surface recombination coefficient is determined at 4 mbar; (2) it has been shown that the surface recombination on the iron electrode is of the second order, and the effective recombination coefficients are determined; (3) the analytical form of the recombination coefficient as a function of the adsorption characteristics of surfaces and the pressure of the parent gas has been derived. In addition, the orders of surface recombination on the molybdenum-, aluminum-, and gold-plated electrode were determined by the same method.     

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.     

具无限时滞的非自治捕食者-食饵系统的持久性

本文采用新的方法研究了具无限时滞的非自治、非卷积的捕食者－食饵系统的持久性问题，得到了新的、有趣的结果。本文的结果包含已知的结果作为特例．