A perturbation theory for the discrete harmonic oscillator equation

This work deals with the existence, uniqueness and stability of solutions for the semilinear discrete harmonic oscillator equation on Banach spaces by using recent characterization of maximal regularity for a best difference approximation of the discrete harmonic oscillator equation.     

稳定性切换在一阶时滞微分方程中的应用

介绍了时滞动力系统中的对零解稳定性讨论的稳定性切换法,并应用此方法对时滞动力系统中的三个一阶时滞微分方程基本定理给予证明.同时表明了在局部稳定性分析中,该方法有着更大的优势.     

A mathematical model describing the thyroid-pituitary axis with time delays in hormone transportation

In the present paper, a mathematical model, originally proposed by Danziger and Elmergreen and describing the thyroid-pituitary homeostatic mechanism, is modified and analyzed for its physiological and clinical significance. The inuence of different system parameters on the stability behavior of the system is discussed. The transportation delays of different hormones in the bloodstream, both in the discrete and distributed forms, are considered. Delayed models are analyzed regarding the stability and bifurcation behavior. Clinical treatment of periodic catatonic schizophrenia is discussed in presence of transportation delays. Numerical simulations are presented to support analytic results.     

A simple proof for the constructions of optical priority queues

Constructions of optical queues by optical Switches and fiber Delay Lines (SDL) have received a lot of attention lately. In this short paper, we provide a simple proof for the construction of a priority queue with a switch and fiber delay lines in Sarwate and Anantharam (Queueing Syst. Theory Appl. 53, 115–125, 2006). Our proof not only gives the insights needed to understand why such a construction works, but also leads to a more general result that recovers the result in Sarwate and Anantharam (Queueing Syst. Theory Appl. 53, 115–125, 2006) as a special case. This research was supported in part by the National Science Council, Taiwan, ROC, under Contract NSC-93-2213-E-007-040, Contract NSC-93-2213-E-007-095, Contract NSC-94-2213-E-007-046, and the Program for Promoting Academic Excellence of Universities NSC 94-2752-E-007-002-PAE.     

Dynamics of a ratio‐dependent stage‐structured predator‐prey model with delay

In this paper, we investigate the dynamics of a time‐delay ratio‐dependent predator‐prey model with stage structure for the predator. This predator‐prey system conforms to the realistically biological environment. The existence and stability of the positive equilibrium are thoroughly analyzed, and the sufficient and necessary conditions for the stability and instability of the positive equilibrium are obtained for the case without delay. Then, the influence of delay on the dynamics of the system is investigated using the geometric criterion developed by Beretta and Kuang. 26 We show that the positive steady state can be destabilized through a Hopf bifurcation and there exist stability switches under some conditions. The formulas determining the direction and the stability of Hopf bifurcations are explicitly derived by using the center manifold reduction and normal form theory. Finally, some numerical simulations are performed to illustrate and expand our theoretical results.     

Global dynamics of a general brucellosis model with discrete delay

For the prevention and control of brucellosis, it is important to investigate the mechanism of brucellosis transmission. Based on the characteristics of the spread of brucellosis, a susceptible-exposed-infectious-brucella (SEIB) delay dynamic model is proposed with the general incidence, elimination rate and shedding rate of pathogen. Under biologically motivated assumptions, it shows the uniqueness of the endemic equilibrium, and investigates the global asymptotically stability of the disease-free equilibrium and the endemic equilibrium. The results suggest that the global stability of equilibria depends entirely on the basic reproduction number $R_0$ and time delay is harmless for the stability of equilibria. Finally, some specific examples and numerical simulations are used to illustrate the utilization of research results and reveal the biological significance of hypothesis $(H_7)$, which implies that the dynamics of brucellosis transmission depend largely on the development of the prevention and control strategies.     

A quantitative study on the stability of delay discrete singular systems

For quadratic delay discrete singular systems, an algebraic criterion on the stability is established, and the size of the uniform stability region and asymptotic stability region around zero is estimated. Hence, the criterion is both qualitative and quantitative. With the computer techniques, the criterion dependent of delay is easy test and applies to the application in the practice. An illustrative simulation is given to illustrate the application of the obtained result.     

Global properties for virus dynamics model with mitotic transmission and intracellular delay

In this paper we study the basic model of viral infections with mitotic transmission and intracellular delay discrete. The delay corresponds to the time between infection of uninfected cells and the emission of virus on a cellular level. By means of Volterra-type Lyapunov functionals, we provide the global stability for this model. Let η be the number of virus produced per infected cell. If ηcrit, the critical number, satisfies η?ηcrit, then the virus-free steady state is globally asymptotically stable. On the contrary if η>ηcrit, then the infected steady state is globally asymptotically stable if a sufficient condition is satisfied.     

Stability and Hopf bifurcation in a predator–prey model with stage structure for the predator

A predator–prey system with stage structure for the predator and time delay due to the gestation of the predator is investigated. By analyzing the corresponding characteristic equations, the local stability of a positive equilibrium and two boundary equilibria of the system is discussed, respectively. Further, the existence of a Hopf bifurcation at the positive equilibrium is also studied. By using an iteration technique and comparison argument, respectively, sufficient conditions are derived for the global stability of the positive equilibrium and one of the boundary equilibria of the proposed system. As a result, the threshold is obtained for the permanence and extinction of the system. Numerical simulations are carried out to illustrate the main results.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Asymptotic Stability for a Class of Neutral Systems with Discrete and Distributed Time Delays

In this note, the asymptotic stability for a class of neutral systems with discrete time and distributed time delays is considered. Delay-dependent criteria are proposed to guarantee the stability for such systems. Some numerical examples are given to illustrate that our results are less conservative than previous results.     

时滞离散网络模型的动力学分析与同步

复杂网络广泛存在于日常生活,首先,给出几类标准的网络模型;然后,利用稳定性控制方法设计并实现了具有时滞与非时滞耦合的复杂网络模型快速控制;最后,通过构造优化Lyapunov函数,讨论其模型的射影同步问题,得到了系统全局稳定的条件和有效的控制器,以实例数值验证其方法的可行性。     

Bifurcations in a delayed differential-algebraic plankton economic system

This paper considers a phytoplankton-zooplankton bio-economic system with delay and harvesting, which is described by differential-algebraic equations. Local stability analysis of the system without delay reveals that a singularity-induced bifurcation phenomenon appears when a variation of the economic interest is taken into account, furthermore, a state feedback controller is designed to stabilize the system at the interior equilibrium. Then, we show that delay, which is considered in the toxic liberation, can induce stability switches, such that the positive equilibrium switches from stability to instability, to stability again and so on. Finally, some numerical simulations are performed to justify analytical findings.     

A model for the homotopy theory of homotopy theory

We describe a category, the objects of which may be viewed as models for homotopy theories. We show that for such models, ``functors between two homotopy theories form a homotopy theory', or more precisely that the category of such models has a well-behaved internal hom-object.

     

Global attractivity in a discrete delay logistic model

1.IntroductionIntherecentworks[l--31,theauthorsconsideredthediscretedelaylogisticmodelIn[3],itwasshownthateverypositivesolutionof(l)oscillatesaboutitspositiveequilibriumx~(a--1)/0ifandonlyifIn[if(seealso[2]),itwasprovedthatiftheneverypositivesolutionof(1)tendstox~(or--1)/pasn-- co.Thepurposeofthispaperistoobtainanothersufficieatconditionforthepositiveequilibriumxof(1)tobeaglobalattractorbyusingamethodverydmerelltfromthatusedin[1,21.Themainresultofthispaperisthefollowingtheorem.*Thisworkispart…     

A connectionist model of the organizational learning curve

Organizational learning can be understood as a spontaneous development of routines. Mathematically, this process can be described as a search for better paths on a graph whose nodes are humans and machines. Since the rules for connecting nodes depend on their ability to process goods, the slope of the learning curve may be connected to physical and psychological properties. Two suggestive examples are discussed. Guido Fioretti, born 1964, graduated in Electronic Engineering and obtained a PhD in Economics from the University of Rome “La Sapienza”. He is currently an assistant professor at the University of Bologna, Italy.His research interests span from decision theory to economics and organization science. In particular, he is interested in linking structural development to cognitive processes. The present article has been conceived as a theoretical underpinning of agent-based simulations of organizations. In particular, future applications of the Java Enterprise Simulator () may test the usefulness of the results derived herein.     

An essay on model theory

Some basic ideas of model theory are presented and a personal outlook on its perspectives is given.     

A mathematical model for continuous crystallization

J. Banasiak We discuss a mixed‐suspension, mixed‐product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.