Collective dynamics induced by diversity taken from two-point distribution in globally coupled chaotic oscillators

The effect of parameter mismatch (diversity) taken from two-point distribution is studied numerically and theoretically in globally coupled Rössler chaotic systems. Two cases including mixed populations consisting of elements with different timescales and attractors are considered. In these two cases, the probability p of two-point distribution, which acts as an asymmetrical coupling on the system, plays a crucial role in determining the evolution of systems, and the rich dynamical phenomena are observed, especially for amplitude death (AD). The relationships between various dynamics are also discussed.     

Random parameters induce chaos in power systems

We study how random parameter (namely, noise-perturbed parameter) effects the dynamical behaviors of power systems using random Melnikov technique and numerical simulation. The studied model is described by the classical single-machine-infinite-bus systems which operate in a stable periodic regime far away from chaotic behavior with deterministic parameter. It is found that when the parameter perturbations are weak, chaos is absent in power systems. With the intensity of random parameter \(\rho \) increasing, power systems become unstable and fall into chaos as \(\rho \) is further increased. These phenomena imply that random parameter can induce and enhance chaos in power systems. Our results may provide a useful tip for understanding power systems’ security operation.     

Parameter identification and synchronization of spatiotemporal chaos in uncertain complex network

Synchronization and parameter identification of a unidirectional star-network constructed by discrete spatiotemporal chaos systems with unknown parameters are studied. The synchronization principle of the network and design method of parameter recognition law are introduced. The function to be determined in the parameter recognition law and the range of adjusting parameter are obtained based on Lyapunov stability theory. Not only global synchronization of the network is realized, but also the unknown parameters in spatiotemporal chaos systems at the nodes of the network are identified. Discrete laser spatiotemporal chaos model is taken as each node of the network, and simulation results show the effectiveness of the synchronization principle and parameter recognition law.     

Parameter estimation for time-delay chaotic systems by hybrid biogeography-based optimization

It is an important issue to estimate parameters of chaotic systems in nonlinear science. In this paper, delay time as well as parameters of time-delay chaotic system is considered by treating delay time as an additional parameter. The parameter estimation problem is formulated as a multidimensional optimization problem, and an effective hybrid biogeography-based optimization is developed to solve this problem. Numerical simulations are conducted on two typical time-delay chaotic systems to show the effectiveness of the proposed scheme.     

A new digital communication scheme based on chaotic modulation

Based on parameter identification, a parameter observer is designed for a class of chaotic systems. The digital signals modulated in the parameter will be recovered by the observer. By choosing different frequency signals as “0” and “1,” a practical digital secure communication scheme is proposed by this parameter modulation method. Numerical simulations show the effectiveness of this communication scheme.     

An estimate for the small parameter in the asymptotic analysis of non-linear systems by the method of averaging

The Method of Averaging is an asymptotic method that can be used to obtain approximate solutions for many parameter dependent non-linear systems. The resulting approximate solutions are as accurate as desired provided the system parameter is sufficiently small. In this paper, a general technique is developed to obtain a relationship between the magnitude of the small parameter and the permissible error in the approximate solution. The technique is then demonstrated by its application to two examples.     

Chaos detection and parameter identification in fractional-order chaotic systems with delay

The paper first applies the 0–1 test for chaos to detecting chaos exhibited by fractional-order delayed systems. The results of the test reveal that there exists chaos in some fractional-order delayed systems with specific parameter values, which coincides with previous reports based on the phase portrait. In addition, it is very important to identify exactly the unknown specific parameters of fractional-order chaotic delayed systems in chaos control and synchronization. Thus, a method for parameter identification of fractional-order chaotic delayed systems based on particle swarm optimization (PSO) is presented. By treating the orders as parameters, the parameters and orders are identified through minimizing an objective function. PSO can efficiently find the optimal feasible solution of the objective function. Finally, numerical simulations on fractional-order chaotic logistic delayed system and fractional-order chaotic Chen delayed system show that the proposed method has effective performance of parameter identification.     

Adhesive contact of an elastic semi-infinite solid with a rigid rough surface: Strength of adhesion and contact instabilities

The effect of adhesion on the contact behavior of elastic rough surfaces is examined within the framework of the multi-asperity contact model of Greenwood and Williamson (1966), known as the GW model. Adhesive surface interaction is modeled by nonlinear springs with a force–displacement relation governed by the Lennard–Jones (LJ) potential. Constitutive models are presented for contact systems characterized by low and high Tabor parameters, exhibiting continuous (stable) and discontinuous (unstable) surface approach, respectively. Constitutive contact relations are obtained by integrating the force–distance relation derived from the LJ potential with a finite element analysis of single-asperity adhesive contact. These constitutive relations are then incorporated into the GW model, and the interfacial force and contact area of rough surfaces are numerically determined. The development of attractive and repulsive forces at the contact interface and the occurrence of instantaneous surface contact (jump-in instability) yield a three-stage evolution of the contact area. It is shown that the adhesion parameter introduced by Fuller and Tabor (1975) governs the strength of adhesion of contact systems with a high Tabor parameter, whereas the strength of adhesion of contact systems with a low Tabor parameter is characterized by a new adhesion parameter, defined as the ratio of the surface roughness to the equilibrium interatomic distance. Applicable ranges of aforementioned adhesion parameters are interpreted in terms of the effective surface separation, obtained as the sum of the effective distance range of the adhesion force and the elastic deformation induced by adhesion. Adhesive strength of rough surfaces in the entire range of the Tabor parameter is discussed in terms of a generalized adhesion parameter, defined as the ratio of the surface roughness to the effective surface separation.     

密频子空间的可控度与可观度

首先提出了频率组的分散度和密集度的概念,从而可以在整体上把握一个频率组的接近程度,然后对于二阶的弹性结构系统,分别在可控性和可观性的意义下,引入了两个同维数的一阶系统,分别以该一维系统为基础,利用小参数方法,以频率组的分散度为参数,分析了密集频率子空间的可控度和可观度,给出了可控度和可观度的一阶近似解。     

Emergence of chaotic regimes in the generalized Lorenz canonical form: a competitive modes analysis

The recently-developed technique of competitive modes analysis is applied to determine parameter regimes for which the generalized Lorenz canonical form, a system constructed by Celikovsky and Chen, which holds many other chaotic systems (such as the Lorenz system, the Lü system, the Chen system, and the Shimizu?CMorioka system), may exhibit chaotic behavior. We verify that the generalized Lorenz canonical form exhibits interesting behaviors in the many parameter regimes thus obtained, thereby demonstrating the great utility of the competitive modes approach in delineating chaotic regimes in multi-parameter systems, where their identification can otherwise involve tedious numerical searches.     

A Modified Perturbation Technique Depending Upon an Artificial Parameter

In this paper, a modified perturbation method is proposed to search for analytical solutions of nonlinear oscillators without possible small parameters. An artificial perturbation equation is carefully constructed by embedding an artificial parameter, which is used as expanding parameter. It reveals that various traditional perturbation techniques can be powerfully applied in this theory. Some examples, such as the Duffing equation and the van der Pol equation, are given here to illustrate its effectiveness and convenience. The results show that the obtained approximate solutions are uniformly valid on the whole solution domain, and they are suitable not only for weak nonlinear systems, but also for strongly nonlinear systems. In applying the new method, some special techniques have been emphasized for different problems.     

Vibrocreep of metals in uniaxial and complex stress states

The results of the creep tests with extension and torsion of tubular specimens made of D16AT and AD1 aluminum alloys, which were earlier obtained at the Institute of Mechanics, Lomonosov State University, were analyzed theoretically. Experimental data obtained with the author’s participation imply that a sharp increase in creep rate is observed under certain conditions when a vibration stress of small amplitude is added to the static stress. This effect (vibrocreep effect) is manifested only if the form of the stress state under the common action of static and dynamic stresses differs from the form of the static stress state. In this case, as the duration of the applied vibration stress increases, the vibrocreep effect gradually weakens. In this paper, we propose a model for describing the obtained experimental data containing the kinetic parameter; this parameter is nonzero only in the case of a complex stress state in the tubular specimens. As a positive measure of this parameter, we use the angle of rotation of the maximum principal stress vector when small vibrations are added to the basic stress state. The obtained experimental and theoretical creep curves are in a good agreement for different types of the stress states.     

随机和区间非齐次线性哈密顿系统的比较研究及其应用

随着计算机技术的飞速发展,更高效、更稳定和长时间模拟能力更强的数值算法需求迫切.哈密顿系统辛算法与传统算法相比在稳定性和长期模拟方面具有显著优越性.但动力系统中不可避免地存在大量不同程度的不确定性,动力学分析中需要考虑这些不确定性的影响以确保合理有效性. 然而,目前考虑参数不确定性的哈密顿系统响应分析的研究基础还比较薄弱. 为此,本文考虑随机和区间参数不确定性,对两种不确定性非齐次线性哈密顿系统分析计算结果进行了比较研究,从而突破了传统哈密顿系统的局限性, 并应用于结构动力响应评估中. 首先,针对确定性非齐次线性哈密顿系统, 提出了考虑确定性扰动的参数摄动法;在此基础上, 分别提出了随机、区间非齐次线性哈密顿系统的参数摄动法,得到了它们响应界限的数学表达; 随后,用数学理论推导得到了区间响应范围包含随机响应范围的相容性结论; 最后,两个数值算例在较小时间步长下验证了所提方法在结构动力响应中的可行性和有效性,体现了随机、区间哈密顿系统响应结果之间的包络关系,并在较大时间步长下与传统方法相比较凸显了哈密顿系统辛算法的数值计算优势、与蒙特卡洛模拟方法相比较验证了所提方法的精度.      

Dynamic buckling of discrete structural systems under combined step and static loads

The dynamic instability of discrete, elastic, multiple degree of freedom (d.o.f.) systems under a combination of static and step loads is studied. Conservative, autonomous and holonomic systems are considered, in which the associated static response is a bifurcation under one load parameter, and a limit point under the second parameter. A review of different criteria and algorithms obtained from them for the computation of dynamic buckling loads is first presented, followed by a procedure derived from previous investigations on one d.o.f. systems. The different procedures are applied to a two d.o.f. problem under axial and lateral load, with quadratic and cubic non-linearities. The response in time shows that the system oscillates about the static equilibrium position before dynamic buckling is reached, with the kinetic energy tending to zero as assumed in the static (energy) procedures of stability.     

Recursive parameter identification of the dynamical models for bilinear state space systems

This paper investigates the recursive parameter and state estimation algorithms for a special class of nonlinear systems (i.e., bilinear state space systems). A state observer-based stochastic gradient (O-SG) algorithm is presented for the bilinear state space systems by using the gradient search. In order to improve the parameter estimation accuracy and the convergence rate of the O-SG algorithm, a state observer-based multi-innovation stochastic gradient algorithm and a state observer-based recursive least squares identification algorithm are derived by means of the multi-innovation theory. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed algorithms.     

Parameter estimation for chaotic systems by hybrid differential evolution algorithm and artificial bee colony algorithm

This paper is concerned with the parameter estimation of nonlinear chaotic system, which could be essentially formulated as a multi-dimensional optimization problem. In this paper, a hybrid algorithm by combining differential evolution with artificial bee colony is implemented to solve parameter estimation for chaotic systems. Hybrid algorithm combines the exploration of differential evolution with the exploitation of the artificial bee colony effectively. Experiments have been conducted on Lorenz system and Chen system. The proposed algorithm is applied to estimate the parameters of two chaotic systems. Simulation results and comparisons demonstrate that the proposed algorithm is better or at least comparable to differential evolution, artificial bee colony, particle swarm optimization, and genetic algorithm from literature when considering the quality of the solutions obtained.     

Synchronization in the Lorenz system: Stability and robustness

We present necessary and sufficient conditions for the existence of synchronization in a class of continuous-time nonlinear systems: the so-called -affine systems. We apply the results to the Lorenz attractor. The robustness of the synchronization against parameter value variations is discussed using the Lyapunov stability theory for perturbed systems. We obtain sufficient conditions that guarantee a bounded steady-state error. This technique gives conservative results; however, in some systems like that of Lorenz, it provides definitive results about the existence of the synchronization. Furthermore, we give estimates of the maximal error as a function of the difference between the parameter values of the systems to be synchronized.     

Generalisation de la methode de la moyenne

A method to reduce some different systems containing a small parameter is proposed. This method makes it possible to regain, in a simple way, the classical method of averaging and to extend it to higher approximations as well as to wider classes of systems. Some examples of applications are then given.     

Parameter identification and chaos synchronization for uncertain coupled map lattices

A method of chaos synchronization and parameter identification is proposed in the paper. The synchronization controller and the parameter recognizer are designed. Two coupled map lattices with different structures are taken as examples to verify the effectiveness of the method. Simulation results show that the identification variables in the parameter recognizer can substitute for the unknown parameters in both target and response systems. Then global synchronization of the two uncertain coupled map lattices can be realized after the designed controller is added.