Existence theorems for some abstract nonlinear non-autonomous systems with delays

For some abstract classes of nonlinear non-autonomous systems with variable and state-dependent delays existence, non-existence and multiplicity of periodic solutions are discussed. To illustrate the efficiency of the method, we obtain some well-known results for applied systems as corollaries of our existence theorems.     

On stability for switched linear positive systems

This paper addresses the stability properties of switched linear positive systems in continuous-time as well as in discrete-time. In the discrete-time case, some sufficient and necessary conditions for asymptotic stability are derived for pairs of second order systems. Similar conditions are also established for a finite number of second order systems. Furthermore, for higher order systems, some results on stability are provided in a similar manner. In particular, in this case, a common linear Lyapunov function guaranteeing the stability of the switched positive systems can be easily located by means of geometry properties. In the continuous-time case, a finite number of second order systems are considered. Some equivalent conditions for stability of such systems are developed.     

On the joint signature of several coherent systems with some shared components

The concept of joint signature (JS), introduced by Navarro, Samaniego, and Balakrishnan (2010), is a useful tool for investigating the joint reliability of two coherent systems with shared components. In this article, by considering several coherent systems which share some components, with independent and identically distributed lifetimes, we obtain a pseudo-mixture representation for the joint distribution of the systems lifetimes based on a general notion of joint signature which is referred to as generalized joint signature (GJS). It is shown how the GJS is separated from the effect of the components’ lifetime distribution and this relationship helps us to represent the GJS as a two-dimensional matrix instead of a high-dimensional one. Based on the GJS, some ordering results are obtained for comparing two clusters of coherent systems with some shared components. Several examples are provided to illustrate the results established here.     

MULTIPLE PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR NONAUTONOMOUS HAMILTONIAN SYSTEMS

This paper studies the existence of periodic solutions for nonautonomous asymptoticallylinear Hamiltonian systems.By using the Z_p index theory some multiplicity results fornonautonomous systems are given,which generalize some results for autonomous systemsdue to Amman and Zenhder.     

Generic bifurcations of low codimension of planar Filippov Systems

In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequences.     

Adaptive synchronization to a general non-autonomous chaotic system and its applications

In this paper, new adaptive synchronous criteria for a general class of n-dimensional non-autonomous chaotic systems with linear and nonlinear feedback controllers are derived. By suitable separation between linear and nonlinear terms of the chaotic system, the phenomenon of stable chaotic synchronization can be achieved using an appropriate adaptive controller of feedback signals. This method can also be generalized to a form for chaotic synchronization or hyper-chaotic synchronization. Based on stability theory on non-autonomous chaotic systems, some simple yet less conservative criteria for global asymptotic synchronization of the autonomous and non-autonomous chaotic systems are derived analytically. Furthermore, the results are applied to some typical chaotic systems such as the Duffing oscillators and the unified chaotic systems, and the numerical simulations are given to verify and also visualize the theoretical results.     

Uniqueness of series with respect to general Franklin systems

We give some sufficient condition for the uniqueness of series with respect to general Franklin systems and discuss analogous results for orthonormal spline systems of higher order and some wavelet systems.     

Optimization and sensitivity analysis of computer simulation models by the score function method

This paper surveys some recent results on the score function (SF) method. This method is suitable for performance evaluation, sensitivity analysis, and optimization of complex discrete-event systems such as non-Markovian queueing systems.     

Rate-monotonic scheduling for hard-real-time systems

Hard-real-time computing systems are widely used in our society, for example, in nuclear and industrial plants, telecommunications, avionics and robotics. In such systems, almost all tasks occur infinitely often and have time deadlines, namely, their correctness relies not only on their logical results, but also on the time at which the results are available. A scheduling algorithm specifies an order in which all the tasks are to be executed, in a way that all the time deadlines are met. This paper provides a review on deterministic scheduling algorithms for hard-real-time systems, focusing mainly on fixed priority, preemptive scheduling of periodic tasks on a single processor and, in particular, on the Rate-Monotonic algorithm. After presenting some basic results, several generalisations, aimed at relaxing some constraints and facing more realistic cases, are described. Issues covered include uniprocessor and multiprocessor systems, periodic and non-periodic tasks, restricted and arbitrary deadlines, fixed and dynamic priorities, independent and synchronised tasks, as well as fault-free and fault-tolerant systems.     

Differential systems, the mapping over period for which is represented by a product of three exponential matrixes

For some periodic differential systems the sufficient conditions of a representation of the mapping over period as a product of a three exponential matrix of the special aspect are obtained. Obtained results are used for research of problems of the existence and stability of periodic solutions of nonlinear systems and the asymptotic orbital stability of cycles of autonomous differential systems.     

The stability of the solutions of a class of integrodifferential systems with infinite delays

Various stability types, analogous to those in the theory of ordinary differential equations, are defined for some classes of integrodifferential systems of equations with infinite delays. Then, on the basis of a variation of constants formula and some results in functional analysis and Laplace transform theory, some necessary conditions and necessary and sufficient conditions are established in order that the trivial solution of a class of systems may be classified as one of the stability types considered in the definitions.     

Limit-periodic solutions of difference and differential systems without global lipschitzianity restrictions

Criteria for the existence of limit-periodic solutions are established to nonlinear difference as well as differential systems governed by a Stepanov-like limit-periodic forcing. The restoring nonlinearities need not be globally Lipschitzean. The obtained sufficient conditions for difference systems are significantly more effective than those for differential systems. Nevertheless, in the continuous case, our theorems also extend some known results. A possibility of more explicit formulations are discussed in concluding remarks.     

Stability, resonance and Lyapunov inequalities for periodic conservative systems

This paper is devoted to the study of Lyapunov type inequalities for periodic conservative systems. The main results are derived from a previous analysis which relates the best Lyapunov constants to some especial (constrained or unconstrained) minimization problems. We provide some new results on the existence and uniqueness of solutions of nonlinear resonant and periodic systems. Finally, we present some new conditions which guarantee the stable boundedness of linear periodic conservative systems.     

单自由度及多自由度系统非平稳随机振动

在文[1]中,对如下所示的非平稳随机过程其中,这里W(t,τ)是系统的单位脉冲响应函数.本文是[1]的继续,我们对单自由度及多自由度系统给出若干结果.     

On parallel multisplitting methods for symmetric positive semidefinite linear systems

In this paper we propose some parallel multisplitting methods for solving consistent symmetric positive semidefinite linear systems, based on modified diagonally compensated reduction. The semiconvergence of the parallel multisplitting method is discussed. The results here generalize some known results for the nonsingular linear systems to the singular systems. Copyright © 2008 John Wiley & Sons, Ltd.     

Weak almost periodic motions,minimality and stability in impulsive semidynamical systems

In this paper, we study topological properties of semidynamical systems whose continuous dynamics are interrupted by abrupt changes of state. First, we establish results which relate various concepts as stability of Lyapunov, weakly almost periodic motions, recurrence and minimality. In the sequel, we study the stability of Zhukovskij for impulsive systems and we obtain some results about uniform attractors.     

Some results on information properties of coherent systems

This paper considers information properties of coherent systems when component lifetimes are independent and identically distributed. Some results on the entropy of coherent systems in terms of ordering properties of component distributions are proposed. Moreover, various sufficient conditions are given under which the entropy order among systems as well as the corresponding dual systems hold. Specifically, it is proved that under some conditions, the entropy order among component lifetimes is preserved under coherent system formations. The findings are based on system signatures as a useful measure from comparison purposes. Furthermore, some results on the system's entropy are derived when lifetimes of components are dependent and identically distributed. Several illustrative examples are also given.     

Uniform stability of switched nonlinear systems

In this paper, we investigate the stability properties of a general class of nonautonomous switched nonlinear systems. Sufficient conditions for uniform stability, uniform asymptotic stability and uniform exponential stability are derived via multiple Lyapunov functions. Our results provide stability criteria for switched systems with both stable and unstable subsystems. Particularly, our results include some existing results as special cases or improve those in the literature. Several numerical examples are worked out to illustrate our results.     

Degenerate elliptic operators diagonal systems and variational integrals

Using a simple quasiconformal transformation of the independent variables it is shown how some regularity results for weak solutions of quasilinear elliptic systems generalize to several cases where the ellipticity of the principal part degenerates. Similarly it is possible to study the regularity of minima of degenerate variational integrals, as well as elliptic equations and systems in unbounded domains.     

The multiplicity of solutions for perturbed second-order Hamiltonian systems with impulsive effects

In this paper, we study the existence of multiple solutions for a class of second-order impulsive Hamiltonian systems. We give some new criteria for guaranteeing that the impulsive Hamiltonian systems with a perturbed term have at least three solutions by using a variational method and some critical points theorems of B. Ricceri. We extend and improve on some recent results. Finally, some examples are presented to illustrate our main results.