A block-by-block method for the impulsive fractional ordinary differential equations

In this paper, a block-by-block numerical method is constructed for the impulsive fractional ordinary differential equations (IFODEs). Firstly, the stability and convergence analysis of the scheme are established. Secondly, the numerical solution which converges to the exact solution with order $3+\gamma$ for $0<\gamma<1$ is proved, where $\gamma$ is the order of the fractional derivative. Finally, a series of numerical examples are carried out to verify the correctness of the theoretical analysis.     

一类中立型脉冲时滞生物模型的正周期解(英文)

运用严格集压缩映射不动点定理,讨论得到了一类中立型脉冲时滞生物模型正周期解存在的充分条件.我们去掉了文[6,7,12-14]周期解存在的一些条件,推广了对应的结果.     

Synchronization of Takagi–Sugeno fuzzy stochastic discrete-time complex networks with mixed time-varying delays

In this paper, we propose and investigate a new general model of fuzzy stochastic discrete-time complex networks (SDCNs) described by Takagi–Sugeno (T–S) fuzzy model with discrete and distributed time-varying delays. The proposed model takes some well-studied models as special cases. By employing a new Lyapunov functional candidate, we utilize some stochastic analysis techniques and Kronecker product to deduce delay-dependent synchronization criteria that ensure the mean-square synchronization of the proposed T–S fuzzy SDCNs with mixed time-varying delays. These sufficient conditions are computationally efficient as it can be solved numerically by the LMI toolbox in Matlab. A numerical simulation example is provided to verify the effectiveness and the applicability of the proposed approach.     

A constant modulus algorithm for blind equalization in α-stable noise

Channel noise is often assumed to be Gaussian in most of the existing channel equalization algorithms. The performance of these algorithms will degrade seriously when the noise is non-Gaussian. This paper deals with the problem of blind channel equalization in impulsive noise environment that is modeled as α-stable process. A modified adaptive error-constrained constant modulus algorithm (MAECCMA) is proposed by soft-limiting the amplitude of the equalizer input and transforming the error signal of the original adaptive error-constrained constant modulus algorithm (AECCMA) nonlinearly to suppress the influence of α-stable noise. Computer simulation results of two underwater acoustic channels show that, MAECCMA has almost the same performance as AECCMA and they both have faster convergence rate than constant modulus algorithm (CMA) and normalized least mean absolute deviation (NLMAD) algorithm in Gaussian noise, while MAECCMA provides the best performance of those four algorithms in α-stable noise.     

Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes

In this Letter, exponential synchronization of a complex network with nonidentical time-delayed dynamical nodes is considered. Two effective control schemes are proposed to drive the network to synchronize globally exponentially onto any smooth goal dynamics. By applying open-loop control to all nodes and adding some intermittent controllers to partial nodes, some simple criteria for exponential synchronization of such network are established. Meanwhile, a pinning scheme deciding which nodes need to be pinned and a simply approximate formula for estimating the least number of pinned nodes are also provided. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network with nonidentical time-delayed dynamical nodes, and an estimate of the upper bound of impulsive intervals ensuring global exponential stability of the synchronization process is also given. Numerical simulations are presented finally to demonstrate the effectiveness of the theoretical results.     

Optimal timing of interventions in fishery resource and pest management

Assuming that a fish population follows the continuous logistic growth or the discrete Beverton-Holt model, several optimal impulsive harvesting policies for the maximum stock level of the fish at the end of a fishing season are investigated under the condition of fixed intensity and frequency of impulsive harvesting. The optimal impulsive harvesting moments for all cases considered are given analytically and the related numerical simulations are also provided. Furthermore, the methods employed can also be used to investigate the optimal timing of chemical control in pest management. Our results confirm that the optimal timing of pesticide applications such that the density of the pest population is minimal at any time during a planting season or the average of density of the pest population over the planting season is minimal is the beginning of the planting season. In practice, the results can be used to guide the fisherman to manage fisheries and guide farmers to control pests.     

A new chaotic system without linear term and its impulsive synchronization

In this paper, a new chaotic system without linear term is presented by ordinary differential equations, and some basic dynamical properties are studied. Moreover, the impulsive synchronization problem of the new chaotic systems is investigated by using uncertain impulsive control matrix. Using the impulsive theory, sufficient conditions are derived for the synchronization of new chaotic systems. Numerical simulation example is provided to verify the effectiveness of the proposed approach.     

Synchronization of time varying delayed complex networks via impulsive control

In this paper, we investigate the problem of synchronization for the time varying delayed complex dynamical networks via impulsive control method, several sufficient synchronization conditions are given, and we consider the impulsive control matrices are time varying delayed matrices. Furthermore, we found impulsive control does not always play an active role in synchronization although impulsive control strategy is cheaper and simpler than other control strategy. Finally, numerical simulations are also given to demonstrate the effectiveness of the proposed schemes.     

模糊自抗扰控制在永磁同步电机调速系统的应用

针对直接转矩调速系统中PID控制器参数鲁棒性差,调速过程中磁链和转矩脉动大的问题,设计了一种基于模糊的改进自抗扰转速控制器;自抗扰策略代替传统的PID控制方法,模糊规则对自抗扰控制算法进行简化,减少待整定参数;与传统的PID控制方法相比,模糊自抗扰控制能提高调速系统的误差估计补偿和抗干扰能力;对比仿真结果,模糊自抗扰控制响应速度快,明显降低了系统在调速过程中的磁链和转矩脉动,表明模糊自抗扰控制具有良好的控制性能,验证了该方法的有效性。     

具有脉冲效应的周期三种群捕食-食饵系统

本文讨论一类具有脉冲效应和周期系数的两个食饵一个捕食者的捕食-食饵系统的动力学行为.利用脉冲微分方程比较定理和乘子理论,证明了系统的有界性,讨论了平凡周期解和半平凡周期解的稳定性,利用重合度的理论给出了系统存在周期正解的充分条件.