统一超混沌系统的投影同步

利用两种方法研究了统一超混沌系统的同步问题.首先以全状态混合投影自适应同步方法,基于Lyapunov稳定性理论,设计了自适应控制器,理论证明了该控制器可以实现参数已知的统一超混沌系统的全状态混合映射同步.其次使用主动控制同步方法,设计了同步控制器,实现了统一超混沌系统的完全同步,最后数值仿真实验进一步验证了所提出方案的有效性. 关键词： 统一超混沌系统 自适应控制器 全状态混合投影同步 主动控制同步     

Adaptive projective synchronization of unified chaotic systems and its application to secure communication

In this paper, a simple adaptive linear feedback control method is proposed for controlling the scaling factor between two coupled unified chaotic systems to a desired value, based on the invarianee principle of differential equations. Under this control strategy, one can arbitrarily select the scaling factor. Numerical simulations are given to support the effectiveness of the proposed method and show the robustness against noise. Furthermore, a secure communication scheme based on the adaptive projective synchronization of unified chaotic systems is presented and numerical simulation shows its feasibility.[第一段]     

New unified formulation of transient phenomena near the instability point on the basis of the fokker-planck equation

A new unified theory of transient phenomena is proposed to treat the passage from an initially unstable state to a final stable state. In the nonlinear intermediate time region, this is reduced to the scaling theory by the present author, and for t→∞ it gives a correct fluctuation asymptotically.     

统一混沌系统的时延模糊控制

在将统一混沌系统表达为T-S模型的基础上, 利用泛函微分方程的Lyapunov-Krasovskii稳定性理论和线性矩阵不等式(LMIs)方法,设计出一个新的带时延状态反馈模糊控制器.仿真结果显示,所设计的控制器能有效地控制统一混沌系统的混沌时间轨迹到其平衡点,且控制简单可靠.     

统一混沌系统的投影同步与控制

对单向耦合的统一混沌系统间的投影同步进行了研究与控制-分析了投影同步现象的产生机 理，给出一方案对投影同步的特征量进行控制-该方案所需控制代价较小, 为设计适当的混 沌信号源提供了一种理论依据，在利用混沌电路系统进行保密通信方面有着一定的应用前景 -仿真实例表明理论分析的正确性和实际控制方案的有效性- 关键词： 统一混沌系统 投影同步 混沌控制 单向耦合     

Robust H∞state estimation for a class of complex networks with dynamic event-triggered scheme against hybrid attacks

We investigate the dynamic event-triggered state estimation for uncertain complex networks with hybrid delays suffering from both deception attacks and denial-of-service attacks.Firstly,the effects of time-varying delays and finitedistributed delays are considered during data transmission between nodes.Secondly,a dynamic event-triggered scheme(ETS)is introduced to reduce the frequency of data transmission between sensors and estimators.Thirdly,by considering the discussed plant,dynamic ETS,state estimator,and hybrid attacks into a unified framework,this framework is transferred into a novel dynamical model.Furthermore,with the help of Lyapunov stability theory and linear matrix inequality techniques,sufficient condition to ensure that the system is exponentially stable and satisfies H∞performance constraints is obtained,and the design algorithm for estimator gains is given.Finally,two numerical examples verify the effectiveness of the proposed method.     

Allometry and growth: A unified view

Allometry is crucial in biology; scaling relations are implied in laws of growth of living systems. The self similarity of Gompertzian growths of biological organisms plays a key role, in this regard, in biological similitude. The origin of allometric relationships and values of the scaling exponents is a source of debate, as well as the origin of the range of biological scales. But, besides biology, scaling and growth characterize many different complex systems. Encompassing these aspects in a unified view is an interesting target. In this paper we propose a coarse but significant model that is applied to astrophysical structures and biological organisms. The inclusion of such different systems suggests applications to fields where allometry is emerging, such as economics, urban planning and the social sciences.     

On unified field theories,dynamical torsion and geometrical models

A new model of a nondualistic unified theory is proposed. This model is absolutely consistent from the mathematical and geometrical points of view and is based on a manifold equipped with an underlying hypercomplex structure and zero nonmetricity. Also we showed that interesting wormhole solutions, similar to the non-Abelian Born-Infeld theory of our previous work [14] can be obtained. The solution of this model is explicitly compared with our previous one and we find that the torsion plays in this unified theory a role similar to that of Yang-Mills type strength field coming from the non-Abelian Born-Infeld energy momentum tensor. The meaning of the Hosoya-Ogura ansatz (namely, the alignment of the isospin with the frame geometry of the space-time) is completely elucidated.     

A model of unified quantum chromodynamics and Yang-Mills gravity

Based on a generalized Yang-Mills framework, gravitational and strong interactions can be unified in analogy with the unification in the electroweak theory. By gauging T (4) × [SU (3)] color in flat space-time, we have a unified model of chromo-gravity with a new tensor gauge field, which couples universally to all gluons, quarks and anti-quarks. The space-time translational gauge symmetry assures that all wave equations of quarks and gluons reduce to a Hamilton-Jacobi equation with the same ’effective Riemann metric tensors’ in the geometric-optics (or classical) limit. The emergence of ef f ective metric tensors in the classical limit is essential for the unified model to agree with experiments. The unified model suggests that all gravitational, strong and electroweak interactions appear to be dictated by gauge symmetries in the generalized Yang-Mills framework.     

Synchronizability of network ensembles with prescribed statistical properties

It has been shown that synchronizability of a network is determined by the local structure rather than the global properties. With the same global properties, networks may have very different synchronizability. In this paper, we numerically studied, through the spectral properties, the synchronizability of ensembles of networks with prescribed statistical properties. Given a degree sequence, it is found that the eigenvalues and eigenratios characterizing network synchronizability have well-defined distributions, and statistically, the networks with extremely poor synchronizability are rare. Moreover, we compared the synchronizability of three network ensembles that have the same nodes and average degree. Our work reveals that the synchronizability of a network can be significantly affected by the local pattern of connections, and the homogeneity of degree can greatly enhance network synchronizability for networks of a random nature.     

Cascade adaptive control of uncertain unified chaotic systems

The chaos control of uncertain unified chaotic systems is considered. Cascade adaptive control approach with only one control input is presented to stabilize states of the uncertain unified chaotic system at the zero equilibrium point. Since an adaptive controller based on dynamic compensation mechanism is employed,the exact model of the unified chaotic system is not necessarily required. By choosing appropriate controller parameters,chaotic phenomenon can be suppressed and the response speed is tunable. Sufficient condition for the asymptotic stability of the approach is derived. Numerical simulation results confirm that the cascade adaptive control approach with only one control signal is valid in chaos control of uncertain unified chaotic systems.     

Top-down approach to unified supergravity models

We introduce a new approach for studying unified supergravity models. In this approach all the parameters of the grand unified theory (GUT) are fixed by imposing the corresponding number of low energy observables. This determines the remaining particle spectrum whose dependence on the low energy observables can now be investigated. We also include some SUSY threshold corrections that have previously been neglected. In particular the SUSY threshold corrections to the fermion masses can have a significant impact on the Yukawa coupling unification.     

Universal local versus unified global scaling laws in the statistics of seismicity

The unified scaling law for earthquakes, proposed by Bak, Christensen, Danon and Scanlon, is shown to hold worldwide, as well as for areas as diverse as Japan, New Zealand, Spain or New Madrid. The scaling functions that account for the rescaled recurrence-time probability densities show a power-law behavior for long times, with a universal exponent about (minus) 2.2. Another decreasing power law governs short times, but with an exponent that may change from one area to another. This is in contrast with a local, time-homogenized version of Bak et al.'s procedure, which seems to present a universal scaling behavior.     

Improving consensus and synchronizability of networks of coupled systems via adding links

The problem of improving the consensus and synchronizability for weighted networks of dynamic systems via adding links among them is investigated in this paper. A weighted network entropy is introduced to measure the homogeneity of the weighted networks. The relationship between the homogeneity and the consensus and synchronizability is analyzed. A solution scheme is proposed to improve the consensus and synchronizability of the weighted networks through maximizing their homogeneity via adding as few links as possible. Weighted networks created from the Barrat model are tested by using the proposed scheme, and two commonly used link-adding approaches are selected to compare with this scheme. Computer simulation results show that the proposed link-adding scheme can enhance the consensus and the synchronizability of the weighted networks effectively and efficiently.     

Radial and Regge excitations in unified,grand unified and subconstituent models

Necessary group theoretic conditions for all elementary gauge bosons and fermions of an arbitrary renormalizable gauge theory to lie on Regge trajectories are reviewed. It is then argued that in properly unified gauge theories all particles of a given spin lie on Regge trajectories. This then implied that a properly unified gauge theory has no local U(1) factor groups, and no massive fermion singlets. A consideration of the general pattern of Regge and radial recurrences to be expected in quantum field theories suggests that the presence or absence of spin $\text{3}\text{2}$ quarks and/or leptons in the TeV region will provide crucial clues to enable one to distinguish between various classes of unified, grand unified, and subconstituent models. The correct interpretation of such excited fermions will require correlation with the Higgs boson mass and possible radial and Regge excitations of the weak vector bosons.     

考虑晶粒分布的多晶体材料超声散射统一理论

现有超声散射统一理论可通过多晶体材料的微观结构和力学特性,实现全频域范围内衰减和相速度的正演建模,但其忽略晶粒尺寸分布的影响,进而降低了正演模型的计算精度.本文对不均匀介质的波动方程进行二阶Keller近似,用全频域格林函数推导介质中的平均波;以截断对数正态分布描述晶粒分布,构建加权的空间相关函数;结合材料的弹性模量协方差,建立含晶粒分布的超声散射统一理论,揭示晶粒分布对超声散射的影响规律;制备304不锈钢试块并开展超声散射实验.结果表明考虑晶粒分布特性后,纵波衰减谱和相速度谱相对于实验结果的相异性降低约49%和64%,横波衰减谱和相速度谱相对于实验结果的相异性降低约12%和4%.可见,本文的统一理论模型能有效修正晶粒分布导致的衰减谱和相速度谱偏差,为晶粒分布反演评价提供理论基础.     

统一非对称光波导横向耦合模理论分析

光波导横向耦合模理论包含正交耦合模理论和非正交耦合模理论两大类, 为了追求形式上的完美, 两类理论没有统一的解析解, 并且都没有对非匹配耦合系统中耦合功率的非对称性进行深入研究. 本文一方面由Helmholtz方程出发推导出了一种新型的非正交耦合模方程, 并对两类理论中的耦合模方程进行了统一处理和求解, 得到了一种统一的解析解; 另一方面根据所得到的统一的解析解对非匹配耦合系统中耦合功率的非对称性进行了详细研究, 计算结果表明非匹配耦合系统中的最大互耦合功率和最小自耦合功率均可用统一的解析解进行近似计算. 关键词： 光波导 耦合模理论 耦合器 最大耦合功率     

Synchronization in power-law networks

We consider realistic power-law graphs, for which the power-law holds only for a certain range of degrees. We show that synchronizability of such networks depends on the expected average and expected maximum degree. In particular, we find that networks with realistic power-law graphs are less synchronizable than classical random networks. Finally, we consider hybrid graphs, which consist of two parts: a global graph and a local graph. We show that hybrid networks, for which the number of global edges is proportional to the number of total edges, almost surely synchronize.     

Synchronization in complex networks with a modular structure

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.