Permanence of a delayed discrete mutualism model with feedback controls

This paper discusses a two species discrete model of mutualism with delays and feedback controls. Sufficient conditions are obtained for the permanence of the system. The results show that feedback control variables have no influence on the persistence property of the system.     

Permanence and existence of periodic solutions for a generalized system with feedback control

Sufficient conditions are obtained for the permanence and the existence of positive periodic solutions of the delay differential system with feedback control

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Existence of almost periodic solution in a ratio-dependent Leslie system with feedback controls

A ratio-dependent Leslie system with feedback controls is studied. By using a comparison theorem and constructing a suitable Lyapunov function, some sufficient conditions for the existence of a unique almost periodic solution (periodic solution) and the global attractivity of the solutions are obtained. Examples show that the obtained criteria are new, general, and easily verifiable.     

Almost periodic solutions of n-species competitive system with feedback controls

In this paper, the following almost periodic n-species competitive system with feedback controls

     

单种群时滞反馈控制生态系统的持久性

利用细致分析的方法对单种群时滞反馈控制生态系统进行研究,获得了该系统正解持久生存的充分条件.     

Existence of periodic solutions for a periodic mutualism model on time scales

By using Mawhin's continuation theorem of coincidence degree theory, sufficient criteria are obtained for the existence of periodic solutions of the mutualism model

     

Global asymptotical stability of a unique almost periodic solution for enterprise clusters based on ecology theory with time-varying delays and feedback controls

This paper is concerned with some dynamic behavior of enterprises cluster constituted by n satellite enterprises and a dominant enterprise. We present a model involving time-varying delays and feedback controls based on ecology theory, which effectively describe the competition and cooperation of enterprises cluster in real economic environments. Applying the comparison theorem of differential equations and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the existence of a unique globally asymptotically stable nonnegative almost periodic solution of the system are obtained. Finally, we present an example to explain the economical significance of mathematical results.     

A new predator-prey model with a profitless delay of digestion and impulsive perturbation on the prey

In this paper, we formulate a robust prey-dependent consumption predator-prey model with a delay of digestion and impulsive perturbation on the prey. Using the discrete dynamical system determined by the stroboscopic map, we obtain a ‘predator-eradication’ periodic solution and show that the ‘predator-eradication’ periodic solution is globally attractive when harvesting for the prey is over certain value. Using a new qualitative analysis method for impulsive and delay differential equations, we prove the system is uniformly persistent when harvesting for the prey is under certain value. Further, we show the delay of digestion is a “profitless” time delay. Moreover, we show our theoretical results by numerical simulation. In this paper, the main feature is that we introduce a delay of digestion and impulsive effects into the predator-prey model and exhibit a new mathematical method which is applied to investigate the system which is governed by both impulsive and delay differential equations.     

Permanence of a discrete nonlinear N-species cooperation system with time delays and feedback controls

A discrete nonlinear N-species cooperation system with time delays and feedback controls is considered in this paper. Sufficient conditions which ensure the permanence of the system are obtained. It is shown that these conditions are weaker than those of Chen [F.D. Chen, Permanence of a discrete N-species cooperation system with time delays and feedback controls, Appl. Math. Comput. 186(2007) 23-29], that is, our investigation shows that the additional condition in Chen’s paper is not necessary.     

Infinite dimensional differential games with hybrid controls

A two-person zero-sum infinite dimensional differential game of infinite duration with discounted payoff involving hybrid controls is studied. The minimizing player is allowed to take continuous, switching and impulse controls whereas the maximizing player is allowed to take continuous and switching controls. By taking strategies in the sense of Elliott-Kalton, we prove the existence of value and characterize it as the unique viscosity solution of the associated system of quasi-variational inequalities.     

On a structural acoustic model which incorporates shear and thermal effects in the structural component

In this paper we consider a structural acoustic model which takes account of thermal effects over and above displacement, rotational inertia and shear effects in the flat flexible structural component of the model. Thus the structural medium is a Reissner-Mindlin plate into which an additional degree of freedom, viz. temperature variation in the plate, has been introduced and the constitutive equations for the structural acoustic model couple parabolic dynamics with hyperbolic dynamics. We show unique solvability of the mathematical model and investigate the effect of the presence of thermal effects on the mechanical dissipation devices needed to attain uniform stabilization of the two-dimensional model in which the structural component is a Timoshenko beam. It turns out that, as in linear structural acoustic models which use the Euler-Bernoulli equation or the Kirchoff equation to describe the deflections of the thermo-elastic structural medium, uniform stabilization of the energy associated with the model can be attained without introducing mechanical dissipation at the free edge of the beam. Open problems with regard to the stabilization of the three-dimensional model are outlined.     

Uniformly Lipschitz feedback optimal controls in a linear-quadratic framework

A uniformly k-Lipschitz feedback optimal control problem is considered in a linear quadratic framework. The value function is derived by a comparison-based reasoning, via which a necessary condition to the existence of optimal solutions is obtained: optimal feedback controls must be linear.     

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.     

THE FEEDBACK DELAY IN DIGITAL CONTROL

It is a fact that the feedback delay actually ariese in digital control systems.It is necessary to modify the structure of digital control systems and develop new control algorithms,which is done in this paper.A great number of digital computer simulation experiments have shown the obvious advantage of the new algorithms.     

Graph completions for impulsive feedback controls

The paper considers impulsive control systems, where the evolution equation depends linearly on the time derivatives of the control function. The basic theory of “graph completions” is here extended to control functions in feedback form. In the case where the control u=u(t,x)$u=u(t,x)$ is piecewise smooth, with a jump along a hypersurface Σ in the t–x space, results are proved on the existence and uniqueness of solutions, and on their approximation by means of smooth feedbacks. The paper is concluded with a couple of examples, concerning the feedback control of mechanical systems by means of active constraints.     

Modeling and analysis of a periodic delayed two-species model of facultative mutualism

In this paper, we propose a periodic delayed two-species system modeling facultative mutualism. By using the method of coincidence degree and Lyapunov functional, easily verifiable sufficient conditions for the existence and globally asymptotic stability of positive periodic solutions of the above system.     

The persistence and global attractivity in general nonautonomous discrete single-species Kolmogorov model with delays

In this paper, general nonautonomous discrete-time single-species Kolmogorov model with delays is studied. Some sufficient conditions on the boundedness, persistence, permanence and global attractivity of solutions are established. As application, the discrete time nonautonomous delayed Allee-effect model is discussed. The sufficient conditions on the permanence and global attractivity are obtained.     

Henry-Gronwall type retarded integral inequalities and their applications to fractional differential equations with delay

This paper presents retarded integral inequalities of Henry-Gronwall type. Applying these inequalities, we study certain properties of solutions to fractional differential equations with delay.