The sterile insect technique in a predator-prey system with monotone functional response

In this paper, we focus on the sterile insect release technique (SIRT) in a predator--prey system with monotone functional response. Unlike most of the existing modeling studies in this field that mainly deal with the pest population only, we have incorporated the predation population as a distinct dynamical equation together with the wild and sterile insect pests. The aim is to investigate the influence of the predation on the SIRT. We use both the continuous model and the impulsive model to carry out a theoretical study, discuss the dynamical behaviour of the model, and compute the critical conditions for eradication of wild insects. We get that both kinds of the predator-prey system with the most popular functional responses Holling type II and III and some other monotone response functions always have the wild insects eradication solution under the certain conditions. Our analytical findings are verified through computer simulation

Discrete Optimal Control Method Based on the Optimal Strategy of Fishing

Consideration was given to the discrete optimal control method for the optimal fishing strategy. Our method is new and efficient for discrete optimal control problem, which is different from the other optimal methods such as the traditional variational method, the Pontryagin principle of maximum, and the dynamic programming. The basic construction of the model is the traditional logistic function relating to the growth of fry. The discrete optimal control method for optimal fishing strategy was used to construct the optimal rate of each fishing strategy; the main focus of our work is on the rigorous mathematical analysis of the optimal control problem. The analysis allows one to obtain the optimal initial investment amount of the fry and the optimal size of the total catch. Furthermore, when the initial investment amount of the fry is below or above the optimal value and the intrinsic growth rate of fish R is too small, we derive that fishing operations should not be started in the last few years to make the overall fishing amount optimal. At last, several typical examples are given to illustrate the obtained results

A new Newton method for convex optimization problems with singular Hessian matrices

In this paper, we propose a new Newton method for minimizing convex optimization problems with singular Hessian matrices including the special case that the Hessian matrix of the objective function is singular at any iteration point. The new method we proposed has some updates in the regularized parameter and the search direction. The step size of our method can be obtained by using Armijo backtracking line search. We also prove that the new method has global convergence. Some numerical experimental results show that the new method performs well for solving convex optimization problems whose Hessian matrices of the objective functions are singular everywhere

Industrial Relations Experiments in China: Balancing Equity and Efficiency the Chinese Way

China should build socialism by "crossing the river by feeling for stones" (Deng Xiaoping). Chinese industrial relations are changing accordingly. Local union experiments have implemented local-level changes experimenting with institutional reforms that address efficiency and equity imbalances. Local union leaders have exercised autonomy to develop multi-employer “community unions” in Changchun’s Chaoyang District to represent peasant migrant workers employed by small firms by targeting small geographic zones and hiring union presidents as organizers, aggregating union members into amalgamated units. While the union’s role still includes social harmonization, unions have undertaken an additional representative role. Similar efforts elsewhere have given the union representation experience. Unions have organized multi-employer federations across industries. Unions also have collaborated with local governments on innovative structures to ensure that companies in some industries, such as construction, post a “bond” to guarantee end-of-year compensation. Finally, this paper discusses the role of the new Labor Contract Law in institutionalizing these changes. The LCL defines more precisely employment relationships and workers’ legal rights and seems to increase unions’ legal authority to ensure that employers respect individual workers’ rights, supports the extension of collective contracts to more enterprises, and appears to give unions greater authority to represent workers within the employment relationship and before legal authorities. These changes may provide a material basis for balancing efficiency with equity. We think these experiments have political foundations, whether it is “harmonious society” or simply to extend the union’s organizing maintain political status. Further research will determine whether these experiments are successful

Robust H∞ Control for Switched Nonlinear System with Multiple Delays

This paper focuses on the problem of robust H∞ control for a class of switched nonlinear systems with multiple time delays which are allowed to appear not only in state but also in input. We will design a controller and a switching law under which the system is “robust stable” and has performance L2-gain γ. Besides, multiple Lyapunov-Razumikhin functions which are relatively less conservative are introduced to investigate the stability of the candidate switched system. In detail, firstly, for uncertain nonlinear switched system with time-varying delays, sufficient condition is given by inequalities which are equivalent to LMIs, so it is easy to be solved; then, as a special case, nonlinear switched system with constant time delay is also considered. Finally, by providing numerical examples, the feasibility of the proposed approach is demonstrated

Controllability Analysis of Linear Time-Varying T-H Equation with Matrix Sequence Method

A satellite is considered to be moving relative to a nominal elliptical orbit, whose dynamics are usually described by the Tschaunner-Hempel equation (T-H equation). In this paper, we propose to transform the second-order time-varying system represented by the linear T-H equation with a second-order matrix form into a first-order time-varying system. Then, the controllability of the first-order time-varying system is investigated with the matrix sequence method including e=0. Meanwhile, we study the observability of the first-order time-varying system with a specific form of measurement. The advantages of the matrix sequence method for controllability and observability analysis are tested by numerical examples, respectively. Dual theory is used to investigate the controllability and observability of the corresponding dual system of the T-H equation. The corresponding conclusions are obtained

Improved Absolute Stability for a Class of Nonlinear Switched Delay Systems via Mode-Dependent Average Dwell Time

In this paper, the absolute stability for a class of switched delay systems with time-varying uncertainties is analyzed. By constructing an appropriate Lyapunov-Krasovskii functional, a new and less conservative criterion is proposed based on the MDADT method. Besides, the idea of N–segmentation is also utilized to make it more flexible to solve the LMIs. Finally, a numerical example is given to show the feasibility and advantages of the method proposed in this paper

A pest control model with birth pulse and residual and delay effects of pesticides

Abstract Pesticides often cause residual and delayed effects on pests. Considering these effects, we use a pollution emission model to simulate the process of spraying pesticides. Many pests reproduce only at a fixed time in a year. So a pest control model with birth pulse and spraying pesticides is proposed. Using the limit system of the developed model, we analyze the dynamics of the system. The stability of the trivial equilibrium and the positive equilibrium of the model is analyzed, and the threshold conditions of pest eradication and permanence of the system are given. We obtain the optimal frequency of spraying pesticides by numerical simulations. The important parameters related to the pest eradication or permanence of the system are given by analyzing the sensitivity of the parameters. Finally, biological explanations are provided