线性时变周期系统的能控性与能稳定性问题

线性时变周期系统是一类普遍存在的重要而又研究较少的系统。介绍了线性时变周期系统的几种应用实例,给出了两种判定时变周期系统能控性与能观性的必要条件,该判别条件的优点是不必计算系统的状态转移矩阵,使判别时变周期系统能控性与能观性简单、高效、易于实现。讨论了时变周期系统在状态反馈下的能稳定性问题,得到了类似于线性定常系统能控性与能稳定性关系的时变周期系统相应结论。说明了结论是线性定常系统相应结论的自然拓展。给出了数值算例的MATLAB仿真求解过程。仿真结果验证了结论的有效性。     

New chaos-based encryption scheme for digital sequence

To enhance the anti-breaking performance of privacy information, this article proposes a new encryption method utilizing the leaping peculiarity of the periodic orbits of chaos systems. This method maps the secret sequence to several chaos periodic orbits, and a short sequence obtained by evolving the system parameters of the periodic orbits in another nonlinear system will be the key to reconstruct these periodic orbits. In the decryption end, the shadowing method of chaos trajectory based on the modified Newton-Raphson algorithm is adopted to restore these system parameters. Through deciding which orbit each pair coordinate falls on, the original digital sequence can be decrypted.     

ALMOST PERIODIC SOLUTION FOR A CLASS OF LOTKA-VOLTERRA TYPE N-SPECIES ECOLOGICAL SYSTEMS WITH TIME DELAY

The uniform permanence and global asymptotic stability of a class of almost periodic Lotka-Volterra type N-species competitive systems with diffusion and delays are investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and new sufficient conditions are obtained for the global asymptotic stability of the unique positive almost periodic solution of the system.     

Dynamical Analysis of a 3-D Chaotic System with only Two Quadratic Nonlinearities

The paper reports the dynamical study of a three-dimensional quadratic autonomous chaotic system with only two quadratic nonlinearities, which is a special case of the so-called conjugate Lue system. Basic properties of this system are analyzed by means of Lyapunov exponent spectrum and bifurcation diagram. The analysis shows that the system has complex dynamics with some interesting characteristics in which there are several periodic regions, but each of them has quite different periodic orbits.     

PERSISTENCE IN A THREE SPECIES LOTKA-VOLTERRA PERIODIC PREDATOR-PREY SYSTEM

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THE PERIODIC HOLLING Ⅱ PREDATOR-PREY MODEL WITH IMPULSIVE EFFECT

In this paper, a periodic Holling II predator-prey model with impulsive effect is investigated. By applying the Floquet theory of linear periodic impulsive equation, some sufficient conditions are obtained for the linear stability and instability of trivial and semi-trivial periodic solutions. Moreover, we use standard bifurcation theory to show the existence of coexistence states which arise near the semi-trivial periodic solution. As an application, we also examine some special case of the system to confirm our main results.     

THE HOPF BIFURCATION DIRECTION OF A FOUR DIMENSIONAL ELECTRONIC NEURAL NETWORK SYSTEM

1.IntroductionCurrentlybifurcationtheoryiswidelyusedinmanymathematicalmodelsofvariousfieldssuchasbiologyjmechanics,medicalscience,managementofnaturalresourcesandthetheoryofneuralnetowrks.Inadifferentialdynamicalsystem,averyimportalltproblemistheexistencea…     

Asymptotic controllability of a class of discrete-time systems with disturbances

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances. It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function. Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system. In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.     

THE ALGEBRAIC CRITERIA FOR THE ASYMPTOTIC BEHAVIOR OF COOPERATIVE SYSTEMS WITH CONCAVE NONLINEARITIES

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptoticbehavior. The global behavior of such a system is completely determined by the sign of allprincipal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions thatthe zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant.except at the origin. The results of Smith under weaker conditions and some applicationsare included.     

从形式结构看辩证法的系统维度

辩证法与系统论的结合，不仅可以从系统论走向辩证法，也可以从辩证法走向系统论。如果把否定之否定规律作为出发点并进行适度抽象而予以形式化，那么，否定之否定过程的“三段式”模式就表现为一个以环节为其结构成分的周期链。以辩证否定的原则来解读这个周期链，可以发现其中隐藏了无数种变易的可能性，“三段式”周期性结构只是其中的一种典型表达式而不是唯一的表达式。事实上，否定之否定的过程是一个具有复杂性维度的系统过程。     

定期保障策略下远航舰艇备件瞬时短缺数评估模型

定期保障条件下远航舰艇备件保障方案规划是海军装备保障工作的重大课题,目前尚未出现有效的解决方法。分析了远航舰艇定期备件保障系统和保障流程,提出了备件瞬时短缺数的定义和数学模型,根据远航舰艇定期保障中自我保障阶段、定期初始保障阶段和定期循环保障阶段的特点,建立了远海舰艇备件定期保障备件瞬时短缺数概率分布模型。最后,通过实例分析,输出结果表明模型能够反映远航舰艇定期保障备件瞬时短缺数的变化规律,可为装备保障指挥人员备件方案决策提供支持。     

一类对称双势阱Duffing系统周期解的衍生与演化

针对自旋单自由度三次强化弹簧—质量振子系统建立的对称双势阱Duffing方程,通过把数值计算与谐波平衡半解析分析相结合,系统分析了该类Duffing系统在谐波强迫激励下周期解随激励频率变化的衍生与演化现象,获得了不同频段谐波强迫激励下系统周期解的类型、周期解的衍生模式与演化规律。分析结果表明,该类Duffing方程存在平衡点临域局部周期解以及鞍结点分岔衍生的对称、反对称与非对称等多种全局周期解;局部或无对称性的全局周期解直接通过倍周期分岔通向混沌运动;全局对称周期一解和反对称周期三次谐波解首先各自发生对称和反对称破缺,再通过倍周期分岔演化为混沌。研究有助于深化对Duffing方程非线性现象及其演化规律的认识。     

计算离散动力系统不稳定周期轨道的精英子空间差异演化算法

通过把探索周期轨道的问题转化为一个非负函数的极小化问题,基于空间收缩的思想,反复重新初始化种群以提高群体的差异性,提高对可行域探测的有效性,提出一类精英子空间差异演化算法求解不同类型非线性映射的不稳定周期轨道,对典型离散动力系统的初步仿真结果表明该算法是一种计算不稳定周期轨道的稳健有效算法.     

PERIODIC SOLUTIONS AND GLOBAL ASYMPTOTIC STABILITY OF A DELAYED DISCRETE PREDATOR-PREY SYSTEM WITH HOLLING II TYPE FUNCTIONAL RESPONSE

In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Hoffing Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.     

Improvement of precision for pendulous integrating gyro accelerometer via adaptive internal model control

An adaptive internal mode control is proposed to eliminate effectively periodic disturbance with uncertain frequency caused by input error angle of PIGA (Pendulous Integrating Gyro Accelerometer). An adaptive algorithm with periodic disturbance frequency identification on line is applied and the internal model controller parameters are adjusted to eliminate disturbance. Then the convergence of this algorithm and the stability of the system are proved by the averaging method. Simulation results verify the proposed scheme can eliminate periodic disturbance and improve the test precision for PIGA effectively.     

船用捷联惯导系统的快速阻尼导航算法

为了消除船用捷联惯性导航系统中的舒勒周期振荡和傅科周期振荡,常用的方法是在水平回路引入阻尼网络。然而,引入阻尼网络之后,系统在达到稳定之前往往需要一个较长的调节时间。系统在调节时间内会有超调等现象,使得系统的性能无法保证。为了减少系统的调节时间,提出一种由逆向解算和正向解算形成的循环算法,导航计算机利用存储的信息在计算机内循环解算,以达到缩短调节时间的目的。最后利用计算机进行仿真实验,结果表明所提方法能够有效缩短阻尼调节时间。     

PERMANENCE AND PERIODIC SOLUTION IN AN INTEGRODIFFERENTIAL SYSTEM WITH DISCRETE DIFFUSION

Dynamical characteristics of an integrodifferential modelling competitive sys-tem with diffusion are investigated.In particular,we derive sufficient conditions for the permanence of species,existence of an attracting periodic solution to the periodic system.The results of Wang Ke in 1994 and 1998 are improved and extended.     

Periodic solution and persistence for a three-species ratio-dependent predator-prey model with time delays in two-patch environments*

The author considers a three-species ratio-dependent predator-prey model with time delay in a two-patch environments. This model is of periodic coefficients, which incorporates the periodicity of the environment. By means of the coincidence degree theory, sufficient conditions for the existence of at least one positive periodic solution of this model are established. Moreover, The author shows that the system is uniformly persistent under the conditions.     

Availability modelling for periodically inspected systems under mixed maintenance policies

The availability of a periodic inspection system under mixed maintenance policies is studied in this paper.To accom-modate the characteristic of multiple failur...     

Logistic脉冲系统的最优脉冲控制

利用脉冲微分方程的周期性理论和最优控制原理,研究了Logistic周期脉冲系统的最优脉冲控制,给出了所研究系统的最佳控制周期和相应的最优捕获量.