Stability results for impulsive pantograph equations

By employing the Lyapunov functions and Razumikhin technique, some stability results are obtained for pantograph equations with impulses. Our results reveal the fact that certain impulses may make an unstable system stable and that the stability of pantograph equations may also be inherited by impulsive pantograph ones under appropriate impulsive perturbations.     

Permanence and global attractivity of an impulsive delay Logistic model

In this paper, we consider an impulsive delay Logistic model. First by mathematical analysis, we obtain the maximum and minimum values of solutions of the corresponding autonomous Logistic model. Then by applying the comparison theorem and constructing some suitable Lyapunov functionals, we discuss the permanence and the global attractivity of the model, based on the boundedness of solutions of the corresponding autonomous Logistic model. An example together with its numerical simulation is given to verify our main result.     

Stability of sets of functional differential equations with impulse effect

In this paper, we investigate stability of sets for a class of impulsive functional differential equations by using piecewise continuous Lyapunov functions with Razumickhin techniques. Some sufficient conditions for stability of sets are established, and some known stability theorems also are generalized.     

Aerodynamics of indirect thrust measurement by the impulse method

The aerodynamic aspects of indirect thrust measurement by the impulse method have been studied both experimentally and numerically. The underlying basic aerodynamic principle is outlined, the phenomena in subsonic, supersonic and arc-heated jets are explored, and factors affecting the accuracy of the method are studied and discussed. Results show that the impulse method is reliable for indirect thrust measurement if certain basic requirements are met, and a simple guideline for its proper application is given.     

The dynamics of an impulsive delay SI model with variable coefficients

An impulsive delayed SI model with variable coefficients and a nonlinear incidence is formulated and analyzed. By introducing three thresholds, we obtain sufficient conditions for eradication and permanence of the disease, respectively. It is shown that the conditions depend on time delay for both the global attractivity of the positive infection-free periodic solution and permanence of the model. Furthermore, our results indicate that the disease will disappear if the ratio of the maximum to minimum of the pulse vaccination rate is lager than some value. The main feature of this paper is that we introduce multi-delays and variable coefficients into the SI model, and exhibit a new method which is applied to investigate this model. Numerical results show that the system we considered has complex dynamics including periodic and quasi-periodic oscillations.     

非线性脉冲向量双曲型微分方程解的H-振动性

研究一类具脉冲时滞的非线性双曲型向量泛函微分方程解的H-振动性.方法是采用由Domslak引进的H-振动性的概念,将向量微分方程解的振动问题转化为纯量微分不等式正解和负解的不存在性问题.得到了解的H-振动性的若干判别准则.     

Optimal payout policy in presence of downside risk

We analyze the determination of a value maximizing dividend payout policy for a broad class of cash reserve processes modeled as spectrally negative jump diffusions. We extend previous results based on continuous diffusion models and characterize the value of the optimal dividend distribution strategy explicitly. We also characterize explicitly the values as well as the optimal dividend thresholds for a class of associated optimal liquidation and sequential lump sum dividend control problems. Our results indicate that both the value as well as the marginal value of the optimal policies are increasing functions of policy flexibility in the discontinuous setting as well.      

Exponential stabilization of nonlinear systems under saturated control involving impulse correction

This paper studies the problem of locally exponential stabilization (LES) of nonlinear systems under a class of hybrid control in the framework of actuator saturation, where the limitation of actuator saturation on both continuous state feedback control and impulsive control are fully considered. Based on impulsive control theory and differential inclusion approach, some sufficient conditions for LES are derived, where a novel set inclusion relation is proposed to handle the double saturation nonlinearities. Different from the existing results that each part of saturated hybrid control (SHC) is required to stabilize the system individually, our results relax the requirement by making full use of the correction effect of the impulse. Moreover, the maximum of estimation of domain of attraction is obtained by a convex optimal problem and corresponding algorithm. The result is applied to the robustness for a class of nonlinear systems. Finally, the validity of the results is shown by two examples and their simulations, where the synchronization problem of Chua’s oscillator is illustrated in the framework of actuator saturation.