ON A PERIODIC PREY-PREDATOR SYSTEM WITH INFINITE DELAYS

Based on the theory of coincidence degree,the existence of positive periodic solutions is established for a periodic prey predator system with infinite delays (t)=x(t)[α(t)-γ(t)y(t)-γ(t)∫ ∞ 0K 1(t,s)y(t-s) d s- ∫ ∞ 0∫ ∞ 0R 1(t,s,θ)y(t-s)y(t-θ) d θ d s], (t)=y(t)[-β(t)+μ(t)x(t)+μ(t)∫ ∞ 0K 2(t,s)x(t-s) d s+ ∫ ∞ 0∫ ∞ 0R 2(t,s,θ)x(t-θ)x(t-s) d θ d s],where α,γ,β,μ are positive continuous ω periodic functions, K i∈C (R×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,.respectively, R i∈C (R×[0,∞)×[0,∞),(0,∞))( i =1,2) are ω periodic with respect to their first arguments,respectively.

Existence of Positive Periodic Solutions of Competitor-Competitor-Mutualist Lotka-Volterra Systems with Infinite Delays

In this paper,the authors primarily explore a delayed competitor-competitor-mutualist Lotka-Volterra model,which is a system of differential equation with infinite integral.The authors first study the existence of positive periodic solutions of the model by using the Krasnoselskii's fixed point theorem,and then present an example to illustrate the main results.

THE STABILITY OF A CLASS OF FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

This paper deals with the problem on the stability for zero solution to a class of functional differential equations with infinite delays. We give up the usual confine to the boundedness of the coefficient matrix of the equations and obtain some new results which guarantee the stability and asymptotic stability for zero solution of the equations. The results are of simple forms, easily checked and applicable, and extend the relative results of [1].

Approximate controllability results of semilinear integrodifferential equations with infinite delays

We study the approximate controllability of control systems governed by a class of semilinear integrod- ifferential equations with infinite delays. Sufficient conditions for approximate controllability of semilinear control systems are established provided the approximate controllability of the corresponding linear control systems. The results are obtained by using fixed-point theorems and semigroup theory. As an illustration of the application of the approximate controllability results, a simple example is provided.

Global Exponential Stability of Fuzzy Cellular Neural Networks with Impulses and Infinite Delays

In this paper, the global exponential stability of fuzzy cellular neural networks with impulses and infinite delays is investigated. Based on an impulsive delayed integro-differential inequality and the properties of fuzzy logic operation and M-matrix, an easily verified sufficient condition is obtained. Moreover, the exponential convergent rate for the fuzzy cellular neural networks with impulses and infinite delays is also given. An example is given to illustrate the effectiveness of our theoretical result.

NOTE ON THE PARTIAL SURVIVAL OF A TWO SPECIES LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH INFINITE DELAYS AND FEEDBACK CONTROLS

A two species Lotka-Volterra competitive system with infinite delays and feedback controls is studied in this paper.By constructing a suitable Lyapunov functional,we show that if the Lotka-Volterra competitive system is bistable(in the absence of feedback controls),then by choosing some suitable values of feedback control variables,one of the species is driven to extinction while the other one becomes globally stable.Examples together with their numerical simulations are presented to verify the feasibility of our results.Our results not only improve but also complement those of Z.Li,M.A.Han and F.D.Chen[Influence of feedback controls on an autonomous Lotka-Volterra competitive system with infinite delays,Nonlinear Anal.:Real World Appl.,14(2013),402-413].

ASYMPTOTIC STABILITY OF NONLINEAR DESCRIPTOR SYSTEMS WITH INFINITE DELAYS

In this paper, the stability problems for a class of nonlinear descriptor systems with infinite delays are investigated. A new Lyapunov second stability criteria is obtained, which is different from linear matrix inequalities (LMIs) method. Finally, a simple example is given to illustrate the main results.

THE EXISTENCE AND UNIQUENESS AND STABILITY OF ALMOST PERIODIC SOLUTIONS FOR FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

This paper deals with the problems on the existence and uniqueness and stability of almost periodic solutions for functional differential equations with infinite delays.The author obtains some sufficient conditions which ganrantee the existence and uniqueness and stability of almost periodic solutions with module containment.The results extend all the results of the paper and solve the two open problems proposed in under much weaker conditions than that proposed in.

Stability for Impulsive Functional Differential Equations with Infinite Delays

In this paper, some theorems of uniform stability and uniform asymptotic stability for impulsive functional differential equations with infinite delay are proved by using Lyapunov functionals and Razumikhin techniques. An example is also proved at the end to illustrate the application of the obtained results.

Stability Criteria of Nonlinear Impulsive Differential Equations with Infinite Delays

In this paper, we consider the uniform stability and uniformly asymptotical stability of nonlinear impulsive infinite delay differential equations. Instead of putting all components of the state variable x in one Lyapunov function, several Lyapunov-Razumikhin functions of partial components of the state variable x are used so that the conditions ensuring that stability are simpler and less restrictive; moreover, examples are discussed to illustrate the advantage of the results obtained.

Pseudo-almost periodic solution for impulsive hematopoiesis model with infinite delays and linear harvesting term

In this paper, a generalized impulsive model of hematopoiesis with infinite delays and linear harvesting term is investigated. The main purpose of this paper is to study the existence, uniqueness and exponential stability of the positive pseudo-almost periodic solutions, which improve and extend some known relevant results. Moreover, an example is given to illustrate the main findings.

GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

Periodic Solutions for a Class of Neutral Functional Differential Equations with Distributed and Discrete Delays

Based on Krasnoselskii's fixed point theorem,matrix measure and functional analysis methods,some new sufficient conditions for the existence of periodic solutions of neutral functional differential equations with distributed and discrete delays are obtained. Moreover,we construct an example to illustrate the feasibility of our results.

Globally Asymptotic Stability of Equilibrium of a Dynamical Model with Infinite Delay

By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.

Periodic Solutions of Singular Neutral Differential Systems with Infinite Delay

In this paper,we discuss the periodic solutions of the nonlinear singular neutral differential systems with infinite delay.By using matrix measure and Krasnoselskii＇s fixed point theorem,we obtained the suffcient conditions of the existence of periodic solutions.

The Existence of Multiple Solutions for Second Order Differential Equations with Infinite Delay

This paper discusses the existence of multiple solutions for second order differential equations with infinite delay.

Global Solutions and Exponential Stability of Stochastic Functional Differential Equations with Infinite Delay

This paper proves that, under the local Lipschitz condition, the stochastic functional differential equations with infinite delay have global solutions without the linear growth condition. Furthermore, the pth moment exponential stability conditions are given. Finally, one example is presented to illustrate our theory.

Onβ-extinction and Stability of a Stochastic Lotka-Volterra System with Infinite Delay

In this paper,a stochastic Lotka-Volterra system with infinite delay is considered.A new concept of extinction,namely,the almost sureβ-extinction is proposed and sufficient conditions for the solution to be almost sureβ-extinction are obtained.When the positive equilibrium exists and the intensities of the noises are small enough,any solution of the system is attracted by the positive equilibrium.Finally,numerical simulations are carried out to support the results.

Improved single image dehazing using dark channel prior

An improved single image dehazing method based on dark channel prior and wavelet transform is proposed. This pro-posed method employs wavelet transform and guided filter instead of the soft matting procedure to estimate and refine the depth map of haze images. Moreover, a contrast enhancement method based on just noticeable difference （JND） and quadratic function is adopted to enhance the contrast for the dehazed image, since the scene radiance is usual y not as bright as the atmospheric light, and the dehazed image looks dim. The experimental results show that the proposed approach can effectively enhance the haze ima-ge and is wel suitable for implementing on the surveil ance and obstacle detection systems.

Fault Detection for Complex Systems with Channel Fadings, Randomly Occurring Multiple Delays and Infinitely Distributed Delays

This paper is concerned with the fault detection（FD） problem for a class of discretetime stochastic systems with channel fadings, randomly occurring multiple communication delays,and infinitely distributed delays. All of the three phenomena have the characteristics of randomly occurring and three sequences of stochastic variables which are mutually independent but obey the Bernoulli distribution are employed to describe them. The aim of this paper is to design an FD filter such that the FD dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Intensive analysis is utilized to derive the sufficient conditions for the designed FD filter, which guarantees the exponential stability and the prescribed H∞ performance. FD filter parameters are obtained by solving a convex optimization problem. An illustrative example is provided to demonstrate the effectiveness of the FD design scheme.