New Approach to Cluster Synchronization in Complex Dynamical Networks

In this paper, a distributed control strategy is proposed to make a complex dynamical network achieve cluster synchronization, which means that nodes in the same group achieve the same synchronization state, while nodes in different groups achieve different synchronization states. The local and global stability of the cluster synchronization state are analyzed. Moreover, simulation results verify the effectiveness of the new approach.     

Local entropic effects of polymers grafted to soft interfaces

In this paper, we study the equilibrium properties of polymer chains end-tethered to a fluid membrane. The loss of conformational entropy of the polymer results in an inhomogeneous pressure field that we calculate for Gaussian chains. We estimate the effects of excluded volume through a relation between pressure and concentration. Under the polymer pressure, a soft surface will deform. We calculate the deformation profile for a fluid membrane and show that close to the grafting point, this profile assumes a cone-like shape, independently of the boundary conditions. Interactions between different polymers are also mediated by the membrane deformation. This pair-additive potential is attractive for chains grafted on the same side of the membrane and repulsive otherwise. Received 20 April 2000     

Description of waves in inhomogeneous domains using Heun’s equation

There are a number of model equations describing electromagnetic, acoustic or quantum waves in inhomogeneous domains and some of them are of the same type from the mathematical point of view. This isomorphism enables us to use a unified approach to solving the corresponding equations. In this paper, the inhomogeneity is represented by a trigonometric spatial distribution of a parameter determining the properties of an inhomogeneous domain. From the point of view of modeling, this trigonometric parameter function can be smoothly connected to neighboring constant-parameter regions. For this type of distribution, exact local solutions of the model equations are represented by the local Heun functions. As the interval for which the solution is sought includes two regular singular points. For this reason, a method is proposed which resolves this problem only based on the local Heun functions. Further, the transfer matrix for the considered inhomogeneous domain is determined by means of the proposed method. As an example of the applicability of the presented solutions the transmission coefficient is calculated for the locally periodic structure which is given by an array of asymmetric barriers.     

On the role of mechanical stress in the chemical ordering of nanoalloys

Metallic alloy clusters at equilibrium display an inhomogeneous stress field which may contribute to the chemical ordering and segregation properties. We use the example of cuboctahedral and icosahedral Au-Pd clusters with the same size to compare these properties in systems displaying moderately and highly inhomogeneous stress fields. Metropolis Monte Carlo simulations in the semi-grand canonical ensemble are used with an empirical potential to predict equilibrium configurations. Pressure maps are used to estimate stress on each atom. It is found that when the stress field is moderately inhomogeneous, ordering is dominantly driven by thermodynamic forces. In icosahedral clusters, ordering is found to be the consequence of a balance where thermodynamic forces and mechanical stress may conflict or reinforce each other. Order-disorder transitions are smoother in the systems with higher stress inhomogeneity and it is conjectured that, in icosahedral clusters, disorder may nucleate in the central core.     

Electric polarization of magnetic textures: New horizons of micromagnetism

A common scenario of magnetoelectric coupling in multiferroics is the electric polarization induced by spatially modulated spin structures. It is shown in this paper that the same mechanism works in magnetic dielectrics with inhomogeneous magnetization distribution: the domain walls and magnetic vortexes can be the sources of electric polarization. The electric field driven magnetic domain wall motion is observed in iron garnet films. The electric field induced nucleation of vortex state of magnetic nanodots is theoretically predicted and numerically simulated. From the practical point of view the electric field control of micromagnetic structures suggests a low-power approach for spintronics and magnonics.     

Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system

This paper is involved with the adaptive control and synchronization problems for an uncertain new hyperchaotic Lorenz system. Based on the Lyapunov stability theory, the adaptive control law is derived such that the trajectory of hyperchaotic Lorenz system with unknown parameters can be globally stabilized to an unstable equilibrium point of the uncontrolled system. Furthermore, an adaptive control approach is presented to the synchronizations between two identical hyperchaotic systems, particularly between two different uncertain hyperchaotic systems. Numerical simulations show the effectiveness of the presented method.     

一类异构多智能体系统固定和切换拓扑下的一致性分析

对包含一阶二阶智能体的异构系统有向图中的一致性问题进行研究.对该系统采用了一种线性分布式一致性协议,基于图论和矩阵分析的方法,分析了在固定和切换拓扑情况下系统获得一致性的充分条件,该条件与控制参数和通信拓扑有关.给出了固定拓扑中系统的一致平衡点,证明了仅通信拓扑中的根节点对平衡点起作用.数值仿真验证了理论分析的正确性.     

Non-linear representations of inhomogeneous groups

We classify the analytic actions, having a fixed point, of the classical inhomogeneous groups, such that the linear part of this action restricted to a Levi factor is the natural action defining this Levi factor as a classical simple group.     

Reconstruction of the stiffness of an inhomogeneous elastic plate

The paper discusses the problem of reconstructing the inhomogeneous cylindrical, symmetric stiffness distribution of a round plate using information on the bias function for established oscillations, which is measured at a certain point. A solution is constructed to the direct problem using the Galerkin method and to the inverse problem of reconstructing the stiffness using an iterative approach based on the regularized linearization method. We present the results of calculation experiments on reconstructing different types of functions that show the efficiency of the proposed approach and make it possible to estimate changes in stiffness.     

Algebraic interpretation of the Yang-Mills field

Einstein's principle of general relativity is a dynamical-group approach in that all dynamics is implied by the invariance and no force is introduced (as an external, symmetry-breaking factor). In this spirit we take a Poincaré-invariant free wave equation and, deforming the Poincaré group to the de Sitter group, obtain interaction. This illustrates our algebraic approach to gauge invariance, whereby the (generalized) Maxwell tensor of the Yang-Mills field appears as structure constants of the homogeneous algebra obtained as a deformation of an inhomogeneous one, with interaction appearing via the same tensor, which plays a role corresponding to the curvature tensor in Einstein's general relativity.     

Generalized potentiality of inhomogeneous media flows

A method for specifying a class of potential flows of inhomogeneous continuous media is developed. The general approach is based on expanding a medium material symmetry group to a special volume-preserving group, allowing us to obtain a law for the conservation of vorticity and, when there is no vorticity, to derive the unsteady Bernoulli equation. As illustrations, plane steady stationary flows of an inhomogeneous incompressible fluid and variable-entropy gas are considered. The problem of an inhomogeneous gas flow around a wedge yielding the formation of a shock wave is solved.     

Cluster projective synchronization of complex networks with nonidentical dynamical nodes

We investigate a new cluster projective synchronization(CPS) scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes.Based on the community structure of the networks,the controllers are designed differently for the nodes in one community,which have direct connections to the nodes in the other communities and the nodes without direct connections to the nodes in the other communities.Some sufficient criteria are derived to ensure the nodes in the same group projectively synchronize and there is also projective synchronization between nodes in different groups.Particularly,the weight configuration matrix is not assumed to be symmetric or irreducible.The numerical simulations are performed to verify the effectiveness of the theoretical results.     

Dynamical robustness analysis of weighted complex networks

Robustness of weighted complex networks is analyzed from nonlinear dynamical point of view and with focus on different roles of high-degree and low-degree nodes. We find that the phenomenon for the low-degree nodes being the key nodes in the heterogeneous networks only appears in weakly weighted networks and for weak coupling. For all other parameters, the heterogeneous networks are always highly vulnerable to the failure of high-degree nodes; this point is the same as in the structural robustness analysis. We also find that with random inactivation, heterogeneous networks are always more robust than the corresponding homogeneous networks with the same average degree except for one special parameter. Thus our findings give an integrated picture for the dynamical robustness analysis on complex networks.     

改进的保群算法及其在混沌系统中的应用

混沌系统的跟踪控制是近年来非线性控制领域研究的热点之一. 本文提出了一种基于快速下降控制方法的保群算法, 此方法使受控混沌系统能够快速稳定到相空间的一个不动点; 另外提出一种基于滑模控制方法的保群算法, 此方法使受控混沌系统能够快速跟踪一个确定的运动轨迹. 应用这两种新方法分别对两个经典的混沌系统(Lorenz系统和Duffing系统)进行了相应的数值实验, 实验结果表明这两种方法都具用较高的精度和稳定性.     

Asymptotic properties of markovian master equations

An asymptotic method of analysis of fluctuations in systems far from equilibrium is developed. A systematic singular perturbative expansion of the equation for the generating function is set up, using as smallness parameter the inverse of the size of the system. Static and time-dependent properties are analysed before, near and at a bifurcation point, both for homogeneous and inhomogeneous fluctuations. The connection with critical phenomena near equilibrium is also discussed.     

Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua's circuits to demonstrate the effectiveness of our proposed approach.     

Symmetry induced compression of discrete phase space

A compressed representation is described of the state space of discrete systems with some kind of symmetry of its states. An initial state space is represented as a network of states. Two states are linked if some single process leads from one state to another. The network can be compressed by a grouping of states into classes. States in the same class are represented by nodes of equal degree. Further, subclasses are defined: states belong to the same subclass if their neighbouring states belong to the same subclasses. The goal is that the equilibrium probability distribution of states in the initial network can be found from the probability of subclasses in the compressed network. The approach is applied to three exemplary systems: two pieces of a triangular lattice (25 and 36 nodes) with Ising spins at the lattice nodes, and a roundabout with three access roads and three exit roads. The compression is from 3630 ground states to 12 subclasses, from 263 640 ground states to 409 subclasses, and from 729 states to 55 subclasses, respectively.     

An algorithm for calculating the chemical potential in associating and reacting fluids

We present a Monte Carlo algorithm to determine the chemical potential of associating and reacting fluids. The algorithm is based on the fact that the chemical potential of a component is the same in the monomer (unbonded) state as in any bonded state. We demonstrate that the chemical potential of the unbonded specie can be calculated at relatively low cost and with high accuracy. The algorithm is applicable to both homogeneous as well as inhomogeneous systems. We compare the results of the presented algorithm against the findings of Widom's single stage particle insertion method for four commonly encountered inhomogeneous systems of associating fluids in phase equilibria studies. The constancy of the chemical potential throughout an inhomogeneous system under equilibrium is used as an independent test of the algorithm. The uncertainty in chemical potential values over the system for the cases studied was on an average 30 times smaller in the new algorithm, with at least 5 times fewer insertions than in the traditional Widom's method.     

A perturbation approach to the propagation characteristics of inhomogeneous optical fibres with deformed core boundaries

The propagation characteristics of inhomogeneous optical fibres with different types of deformed core boundaries are analysed by a perturbative approach based on the scalar wave equation. The influence of the core deformation on the propagation constants and group delays is studied in detail for the truncated parabolic profile. We can conclude from this analysis that the difference in group delays due to deviation from circularity does not cause any difficult tolerance problems for realistic deformations and is generally negligible for practical optical fibres.     

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.