OPTIMAL IMPULSIVE CONTROL IN COMPETITIVE SYSTEM

In this paper,the impulsive exploitation of two species periodic competitive system is considered.First,we show that this type of system with impulsive har- vesting has a unique positive periodic solution,which is globally asymptotically stable.Further,by choosing the maximum total revenues as the management objective,we investigate the optimal harvesting policies for periodic competi- tive system with impulsive harvesting.Finally,we obtain the optimal time to harvest and optimal population level.     

具有脉冲效应和综合害虫控制的捕食系统

本文通过生物控制和化学控制提出了具有周期脉冲效应与害虫控制的捕食系统. 系统保护天敌避免灭绝,在一些条件下可以使害虫灭绝.就是说当脉冲周期小于某一临界值时,存在全局稳定害虫灭绝周期解.脉冲周期增大大于临界值时,平凡害虫灭绝周期解失去稳定性并产生正周期解,利用分支理论来研究正周期解的存在性.进而,利用李雅普诺夫函数和比较定理确定了持续生存的条件.     

一类脉冲时滞双曲型方程组解的振动性

本文研究含脉冲的时滞双曲型方程组解的振动性,利用二阶脉冲微分不等式的性质,得到了方程组在两类不同边界条件下解振动的一些充分判据.     

ON THE PARTIAL STABILITY OF IMPULSIVE DIFFERENTIAL EQUATIONS

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具有非单调功能反应和脉冲扰动的捕食系统的研究

研究捕食者具有非单调功能反应和周期脉冲扰动的捕食者一食饵系统，利用脉冲微分方程的Floquet理论和比较定理，得到了系统灭绝和持续生存的充分条件．最后，通过数值模拟阐明系统在周期脉冲扰动下的复杂性．     

THE UNIQUENESS OF SOLUTION FOR A KIND OF NONLINEAR IMPULSIVE INTEGRODIFFERENTIAL EQUATION

In this paper, we discuss the uniqueness of solutions for a kind of impulsive differential equations, and obtain the successive sequence of solution and the error estimate of convergence rate.     

GENERIC OSCILLATIONS OF FIRST ORDER IMPULSIVE DELAY DIFFERENTIAL EQUATIONS

In this paper, we will study generic oscillation and generic nonoscillation of first order impulsive delay differential equations. A necessary and sufficient condition and some sufficient conditions are obtained for both phenomena based on the root of characteristic equation.     

MODELING DYNAMICS OF FISHERY HARVEST REALLOCATIONS: AN ANALYSIS OF THE NORTH CAROLINA RED DRUM FISHERY

The interactive dynamics of red drum stock growth and two-sector harvest are modeled as a system of differential equations. The dynamic effects of commercial harvest restrictions on stock growth and recreational catch and effort are simulated. The simulation shows that a reallocation of the North Carolina red drum stock from the commercial sector to the recreational sector will not only increase benefits to the recreational sector, but will also be stock enhancing. Stock growth in the years immediately following the reallocation is quite rapid, with complete transition to the final steady-state taking between 23 and 46 years. Parameters important to the behavior of the system are identified through sensitivity analysis, and are used to establish critical areas for further research.     

DISSIPATIVITY BEHAVIOR OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper,we investigate the dissipativity behavior and give the range estimate for solutions of impulsive functional differential equations.Also,some criteria on asymptotical stability and exponential stability of the zero solution are obtained.     

STRICT STABILITY OF IMPULSIVE SET VALUED DIFFERENTIAL EQUATIONS

In this paper, we develop strict stability concepts of ODE to impulsive hybrid set valued differential equations. By Lyapunov’s original method, we get some basic strict stability criteria of impulsive hybrid set valued equations.     

OPTIMAL HARVESTING OF A SPATIALLY EXPLICIT FISHERY MODEL

Abstract We consider an optimal fishery harvesting problem using a spatially explicit model with a semilinear elliptic PDE, Dirichlet boundary conditions, and logistic population growth. We consider two objective functionals: maximizing the yield and minimizing the cost or the variation in the fishing effort (control). Existence, necessary conditions, and uniqueness for the optimal harvesting control for both cases are established. Results for maximizing the yield with Neumann (no‐flux) boundary conditions are also given. The optimal control when minimizing the variation is characterized by a variational inequality instead of the usual algebraic characterization, which involves the solutions of an optimality system of nonlinear elliptic partial differential equations. Numerical examples are given to illustrate the results.     

具脉冲效应的时滞周期捕食与被捕食系统正周期解的存在性

本文研究一类具脉冲效应的时滞周期捕食与被捕食系统，利用重合度理论中的方法，获得该系统至少存在一个正周期解的充分条件。     

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.     

OSCILLATION OF FIRST ORDER NONLINEAR IMPULSIVE DIFFERENTIAL EQUATIONS WITH MIXED ARGUMENT

This paper devotes to study the oscillatory behavior of solutions of a first order nonlinear impulsive differential equation with mixed argument. First, without assuming the deviating argument to be retarded or advanced, a sufficient condition is established for all solutions of the differential equation to be oscillatory. Next, a sufficient condition for the differential equation to have nonoscillatoty solution is given. Finally, a sufficient and necessary condition for all solutions of the differential equation to be oscillatory is obtained.     

BOUNDEDNESS OF IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

In this paper, we study the boundedness of a class of impulsive functional differential equations with infinite delays. We establish a uniform boundedness theorem and a uniformly ultimate boundedness theorem, which show that a certain impulsive perturbation can make an unbounded system into uniformly bounded, even uniformly ultimate bounded.     

NECESSARY AND SUFFICIENT CONDITION FOR OSCILLATION OF IMPULSIVE DELAY HYPERBOLIC DIFFERENTIAL SYSTEM

This paper deals with the oscillation problems of impulsive delay hyperbolic system.A necessary and sufficient condition is obtained.     

OSCILLATION CRITERIA FOR HIGHER-ORDER IMPULSIVE HYPERBOLIC SYSTEM WITH DISTRIBUTED DEVIATING ARGUMENTS

By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.     

INTEGRATED BISEMIGROUP AND APPLICATIONS TO IMPULSIVE DIFFERENTIALEQUATIONS

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脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.     

带强迫项的n阶脉冲微分方程的振动性与渐近性

给出引理,解决了一类带强迫项的n阶脉冲微分方程的非振动解与其各阶导数的符号关系,得到其振动性与渐近性的判别准则,并举例说明准则的有效性.