食物有限的时滞种群模型的振动性

将考虑两类具有变时滞非线性有限食物种群模型N′(t)=r(t)N(t)K-N(p(t))/K+s(t)N(σ(t)),t≥ 0和N′(t)=r(t)N(t)K-Nα(p(t))/K+s(t)Nα(σ(t)),t≥ 0,的振动性,其中α>0,ρ(t)≤t,σ(t)≤t.我们的工作推广并改进了相关文献的结果.     

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.     

Exponential Stability of Singularly Perturbed Systems with Time Delay

In this article, we study the exponential stability of singularly perturbed systems with time delay. By using vector delay inequalities and Lyapunov functions, exponential stability criteria are derived for both linear and some classes of nonlinear singularly perturbed systems with time delay. Examples are given to verify the stability criteria.     

Delay‐dependent criteria on the global attractivity of Nicholson's blowflies model with patch structure

In this paper, we investigate the effect of delay on the asymptotic behavior of Nicholson's blowflies model with patch structure and multiple time‐varying delays. By using the fluctuation lemma and some differential inequality technique, delay‐dependent criteria are obtained for the global attractivity of the addressed system. Meanwhile, some numerical examples are given to illustrate the feasibility of the theoretical results. Copyright © 2017 John Wiley & Sons, Ltd.     

Temporal and spatiotemporal variations in a mathematical model of macrophage–tumor interaction

In the present paper we study a three-component mathematical model of tumor–immune system interaction. A number of solid tumors contain a high proportion of macrophages and these immune cells are known to have a remarkable impact on the progression and dormancy of such tumors. We assume these macrophages as the main immune system component facilitating tumor destruction. Stability criteria of the basic model around the steady state of coexistence are derived. Next, we consider the process of macrophage activation as non-instantaneous by using a distributed delay with a weak kernel and obtain a range for the macrophage death rate that ensures system stability. Finally, we incorporate the spatial irregularity of solid tumors by making the delay nonlocal. Analysis of the resulting spatiotemporal model gives a number of thresholds in terms of different system parameters that guarantee tumor stability. Numerical simulations are performed to justify analytical findings.     

Ratio dependent predation :A bifurcation analysis

In this study, we have considered a prey-predator model reflecting the predator interference with discrete time delay. This delay is regarded as the lag due to gestation. In absence of delay, the criteria for existence of interior equilibrium and its global stability are derived. By choosing the delay as a bifurcation parameter, we have shown that a Hopf bifurcation may occur when the delay passes its critical value. Finally, we have derived the criteria for stability switches and verified the results through computer simulation.     

Dynamical behaviors on a delay differential neoclassical growth model with patch structure

In this paper, by applying the fluctuation lemma and some differential inequality technique, delay‐dependent criteria are obtained for the global attractivity of a differential neoclassical growth model with patch structure and multiple time‐varying delays. Moreover, some numerical examples are provided to illustrate the validity of the obtained results.     

Stability and Hopf bifurcations in a business cycle model with delay

In this paper, a business cycle model with discrete delay is considered. We first investigate the stability of the equilibrium and the existence of Hopf bifurcations, and then the direction and the stability criteria of the bifurcating periodic solutions are obtained by the normal form theory and the center manifold theorem. This research has an important theoretical value as well as practical meaning.     

Stability analysis for neutral systems with mixed delays

Relationships between system states contained in the neutral equation are used to address the delay-dependent stability of a neutral system with time-varying state delay. Using linear matrix inequalities, we present a new asymptotic stability criterion, and a new robust stability criterion, for neutral systems with mixed delays. Since the criteria take into account the sizes of the neutral delay, discrete delay and the derivative of discrete delay, they are less conservative than those produced by previous approaches. Numerical examples are presented to demonstrate that these criteria are indeed more effective.     

Modeling the role of constant and time varying recycling delay on an ecological food chain

We consider a mathematical model of nutrient-autotroph-herbivore interaction with nutrient recycling from both autotroph and herbivore. Local and global stability criteria of the model are studied in terms of system parameters. Next we incorporate the time required for recycling of nutrient from herbivore as a constant discrete time delay. The resulting DDE model is analyzed regarding stability and bifurcation aspects. Finally, we assume the recycling delay in the oscillatory form to model the daily variation in nutrient recycling and deduce the stability criteria of the variable delay model. A comparison of the variable delay model with the constant delay one is performed to unearth the biological relevance of oscillating delay in some real world ecological situations. Numerical simulations are done in support of analytical results.     

非线性退化时滞微分控制系统的函数能控性

本文讨论非线性退化时滞微分控制系统．首先就非线性退化时滞微分控制系统的一阶变分系统给出变易公式,然后就非线性退化时滞微分控制系统的一阶变分系统的函数能控性给出一些判据,最后给出关于非线性退化时滞微分控制系统的函数能控性的判据．     

Boundedness and global exponential stability for delayed differential equations with applications

The boundedness of solutions for a class of n-dimensional differential equations with distributed delays is established by assuming the existence of instantaneous negative feedbacks which dominate the delay effect. As an important by-product, some criteria for global exponential stability of equilibria are obtained. The results are illustrated with applications to delayed neural networks and population dynamics models.     

Stability analysis of highly nonlinear hybrid multiple-delay stochastic differential equations

Stability criteria for stochastic differential delay equations (SDDEs) have been studied intensively for the past few decades. However, most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability of highly nonlinear hybrid stochastic differential equations with a single delay is investigated in [Fei, Hu, Mao and Shen, Automatica, 2017], whose work, in this paper, is extended to highly nonlinear hybrid stochastic differential equations with variable multiple delays. In other words, this paper establishes the stability criteria of highly nonlinear hybrid variable multiple-delay stochastic differential equations. We also discuss an example to illustrate our results.     

Robust stability analysis of uncertain systems with two additive time-varying delay components

This paper is concerned with stability analysis for uncertain systems. The systems are based on a new time-delay model proposed recently, which contains multiple successive delay components in the state. The relationship between the time-varying delay and its upper bound is taken into account when estimating the upper bound of the derivative of Lyapunov functional. As a result, some less conservative stability criteria are established for systems with two successive delay components and parameter uncertainties. Numerical examples show that the proposed criteria are effective and are an improvement over some existing results in the literature.     

Positive periodic solution for a neutral Logarithmic population model with feedback control

In this paper, a neutral delay Logarithmic population model with feedback control is studied. By using the abstract continuous theorem of k-set contractive operator, some new results on the existence of the positive periodic solution are obtained; after that, by constructing a suitable Lyapunov functional, a set of easily applicable criteria is established for the global asymptotically stability of the positive periodic solution.     

Stochastic functional differential equations with infinite delay

The stability and boundedness of the solution for stochastic functional differential equation with finite delay have been studied by several authors, but there is almost no work on the stability of the solutions for stochastic functional differential equations with infinite delay. The main aim of this paper is to close this gap. We establish criteria of pth moment ψγ(t)-bounded for neutral stochastic functional differential equations with infinite delay and exponentially stable criteria for stochastic functional differential equations with infinite delay, and we also illustrate the result with an example.     

New LMI-based criteria for global robust stability of delayed neural networks

Some novel, linear matrix inequality based, criteria for the uniqueness and global robust stability of the equilibrium point of Hopfield-type neural networks with delay are presented. A comparison of the present criteria with the previous criteria is made.     

Stability of impulsive stochastic differential delay systems and its application to impulsive stochastic neural networks

This paper is concerned with the stability of n-dimensional stochastic differential delay systems with nonlinear impulsive effects. First, the equivalent relation between the solution of the n-dimensional stochastic differential delay system with nonlinear impulsive effects and that of a corresponding n-dimensional stochastic differential delay system without impulsive effects is established. Then, some stability criteria for the n-dimensional stochastic differential delay systems with nonlinear impulsive effects are obtained. Finally, the stability criteria are applied to uncertain impulsive stochastic neural networks with time-varying delay. The results show that, this convenient and efficient method will provide a new approach to study the stability of impulsive stochastic neural networks. Some examples are also discussed to illustrate the effectiveness of our theoretical results.     

Stability of highly nonlinear hybrid stochastic integro-differential delay equations

For the past few decades, the stability criteria for the stochastic differential delay equations (SDDEs) have been studied intensively. Most of these criteria can only be applied to delay equations where their coefficients are either linear or nonlinear but bounded by linear functions. Recently, the stability criterion for highly nonlinear hybrid stochastic differential equations is investigated in Fei et al. (2017). In this paper, we investigate a class of highly nonlinear hybrid stochastic integro-differential delay equations (SIDDEs). First, we establish the stability and boundedness of hybrid stochastic integro-differential delay equations. Then the delay-dependent criteria of the stability and boundedness of solutions to SIDDEs are studied. Finally, an illustrative example is provided.     

Some sufficient conditions for oscillation of impulsive delay hyperbolic systems with Robin boundary conditions

This paper deals with the oscillation problems of delay hyperbolic systems with impulses. Some sufficient conditions for oscillations of impulsive delay hyperbolic systems with Robin boundary conditions are obtained and the criteria of oscillation of the systems are established.