arXiv subjects

Ying-Cheng Lai

Publications and source records attributed to Ying-Cheng Lai.

143 records · Page 8Linked to original sources

arXiv2007

Enhancing synchronization in complex networks of coupled phase oscillators

By a model of coupled phase oscillators, we show analytically how synchronization in {\em non-identical} complex networks can be enhanced by introducing a proper gradient into the couplings. It is found that, by pointing the gradient from the large-degree to the small-degree nodes on each link, increasing the gradient strength will bring forward the {\em onset} of network synchronization monotonically, and, under the same gradient strength, heterogeneous networks are more synchronizable than homogeneous networks. These findings are verified by extensive simulations.

nlin.CD↗

arXiv2007

Optimization of synchronization in gradient clustered networks

We consider complex clustered networks with a gradient structure, where sizes of the clusters are distributed unevenly. Such networks describe more closely actual networks in biophysical systems and in technological applications than previous models. Theoretical analysis predicts that the network synchronizability can be optimized by the strength of the gradient field but only when the gradient field points from large to small clusters. A remarkable finding is that, if the gradient field is sufficiently strong, synchronizability of the network is mainly determined by the properties of the subnetworks in the two largest clusters. These results are verified by numerical eigenvalue analysis and by direct simulation of synchronization dynamics on coupled-oscillator networks.

nlin.CD↗

arXiv2007

The multiple effects of gradient coupling on network synchronization

Recent studies have shown that synchronizability of complex networks can be significantly improved by asymmetric couplings, and increase of coupling gradient is always in favor of network synchronization. Here we argue and demonstrate that, for typical complex networks, there usually exists an optimal coupling gradient under which the maximum network synchronizability is achieved. After this optimal value, increase of coupling gradient could deteriorate synchronization. We attribute the suppression of network synchronization at large gradient to the phenomenon of network breaking, and find that, in comparing with sparsely connected homogeneous networks, densely connected heterogeneous networks have the superiority of adopting large gradient. The findings are supported by indirect simulations of eigenvalue analysis and direct simulations of coupled nonidentical oscillator networks.

nlin.AO↗

arXiv2007

Synchronization in Gradient Networks

The contradiction between the fact that many empirical networks possess power-law degree distribution and the finding that network of heterogeneous degree distribution is difficult to synchronize has been a paradox in the study of network synchronization. Surprisingly, we find that this paradox can be well fixed when proper gradients are introduced to the network links, i.e. heterogeneity is in favor of synchronization in gradient networks. We analyze the statistical properties of gradient networks and explore their dependence to the other network parameters. Based on these understandings, we further propose a new scheme for network synchronization distinguished by using less network information while reaching stronger synchronizability, as supported by analytical estimates of eigenvalues and directed simulations of coupled chaotic oscillators. Our findings suggest that, with gradient, scale-free network is a natural choice for synchronization.

nlin.CD↗

arXiv2006

Oscillations of complex networks

A complex network processing information or physical flows is usually characterized by a number of macroscopic quantities such as the diameter and the betweenness centrality. An issue of significant theoretical and practical interest is how such a network responds to sudden changes caused by attacks or disturbances. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to \emph{oscillate} persistently in the sense that the characterizing quantities vary periodically or randomly with time. We provide a theoretical estimate of the critical capacity-parameter value for the onset of the network oscillation. The finding is expected to have broad implications as it suggests that complex networks may be structurally highly dynamic.

cond-mat.stat-mech↗

arXiv2003

Reactive dynamics of inertial particles in nonhyperbolic chaotic flows

Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular enhancement of the production caused by the universal, underlying fractal patterns. The key dynamical invariant quantities are the effective fractal dimension and effective escape rate, which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets. The theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case. We introduce a class of dissipative embedding maps for numerical verification.

nlin.CD↗

arXiv2003

Large-scale structural organization of social networks

The characterization of large-scale structural organization of social networks is an important interdisciplinary problem. We show, by using scaling analysis and numerical computation, that the following factors are relevant for models of social networks: the correlation between friendship ties among people and the position of their social groups, as well as the correlation between the positions of different social groups to which a person belongs.

cond-mat.dis-nn↗

arXiv2003

Heterogeneity in oscillator networks: Are smaller worlds easier to synchronize?

Small-world and scale-free networks are known to be more easily synchronized than regular lattices, which is usually attributed to the smaller network distance between oscillators. Surprisingly, we find that networks with a homogeneous distribution of connectivity are more synchronizable than heterogeneous ones, even though the average network distance is larger. We present numerical computations and analytical estimates on synchronizability of the network in terms of its heterogeneity parameters. Our results suggest that some degree of homogeneity is expected in naturally evolved structures, such as neural networks, where synchronizability is desirable.

cond-mat.dis-nn↗

arXiv2003

Signatures of small-world and scale-free properties in large computer programs

A large computer program is typically divided into many hundreds or even thousands of smaller units, whose logical connections define a network in a natural way. This network reflects the internal structure of the program, and defines the ``information flow'' within the program. We show that, (1) due to its growth in time this network displays a scale-free feature in that the probability of the number of links at a node obeys a power-law distribution, and (2) as a result of performance optimization of the program the network has a small-world structure. We believe that these features are generic for large computer programs. Our work extends the previous studies on growing networks, which have mostly been for physical networks, to the domain of computer software.

cond-mat.dis-nn↗

arXiv2003

Strange nonchaotic attractors in noise driven systems

Strange nonchaotic attractors (SNAs) in noise driven systems are investigated. Before the transition to chaos, due to the effect of noise, a typical trajectory will wander between the periodic attractor and its nearby chaotic saddle in an intermittent way, forms a strange attractor gradually. The existence of SNAs is confirmed by simulation results of various critera both in map and continuous systems. Dimension transition is found and intermittent behavior is studied by peoperties of local Lyapunov exponent. The universality and generalization of this kind of SNAs are discussed and common features are concluded.

nlin.CD↗

arXiv2003

Cascade-based attacks on complex networks

We live in a modern world supported by large, complex networks. Examples range from financial markets to communication and transportation systems. In many realistic situations the flow of physical quantities in the network, as characterized by the loads on nodes, is important. We show that for such networks where loads can redistribute among the nodes, intentional attacks can lead to a cascade of overload failures, which can in turn cause the entire or a substantial part of the network to collapse. This is relevant for real-world networks that possess a highly heterogeneous distribution of loads, such as the Internet and power grids. We demonstrate that the heterogeneity of these networks makes them particularly vulnerable to attacks in that a large-scale cascade may be triggered by disabling a single key node. This brings obvious concerns on the security of such systems.

cond-mat.dis-nn↗

arXiv2003

Range-based attack on links in scale-free networks: are long-range links responsible for the small-world phenomenon?

The small-world phenomenon in complex networks has been identified as being due to the presence of long-range links, i.e., links connecting nodes that would otherwise be separated by a long node-to-node distance. We find, surprisingly, that many scale-free networks are more sensitive to attacks on short-range than on long-range links. This result, besides its importance concerning network efficiency and/or security, has the striking implication that the small-world property of scale-free networks is mainly due to short-range links.

cond-mat.dis-nn↗

arXiv2002

Smallest small-world network

Efficiency in passage times is an important issue in designing networks, such as transportation or computer networks. The small-world networks have structures that yield high efficiency, while keeping the network highly clustered. We show that among all networks with the small-world structure, the most efficient ones have a single ``center'', from which all shortcuts are connected to uniformly distributed nodes over the network. The networks with several centers and a connected subnetwork of shortcuts are shown to be ``almost'' as efficient. Genetic-algorithm simulations further support our results.

cond-mat.dis-nn↗

arXiv2002

Topology of the conceptual network of language

We define two words in a language to be connected if they express similar concepts. The network of connections among the many thousands of words that make up a language is important not only for the study of the structure and evolution of languages, but also for cognitive science. We study this issue quantitatively, by mapping out the conceptual network of the English language, with the connections being defined by the entries in a Thesaurus dictionary. We find that this network presents a small-world structure, with an amazingly small average shortest path, and appears to exhibit an asymptotic scale-free feature with algebraic connectivity distribution.

cond-mat.dis-nn↗

arXiv2002

Cusp-scaling behavior in fractal dimension of chaotic scattering

A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal dimension of the chaotic set for such a bifurcation. Our analysis and numerical computations in both two- and three-degrees-of-freedom systems suggest a striking feature associated with these subtle bifurcations: the dimension typically exhibits a sharp, cusplike local minimum at the bifurcation.

nlin.CD↗

arXiv2000

Validity of threshold-crossing analysis of symbolic dynamics from chaotic time series

A practical and popular technique to extract the symbolic dynamics from experimentally measured chaotic time series is the threshold-crossing method, by which an arbitrary partition is utilized for determining the symbols. We address to what extent the symbolic dynamics so obtained can faithfully represent the phase-space dynamics. Our principal result is that such practice leads to a severe misrepresentation of the dynamical system. The measured topological entropy is a Devil's staircase-like, but surprisingly nonmonotone, function of a parameter characterizing the amount of misplacement of the partition.

nlin.CD↗

arXiv1999

Efficient algorithm for detecting unstable periodic orbits in chaotic systems

We present an efficient method for fast, complete, and accurate detection of unstable periodic orbits in chaotic systems. Our method consists of a new iterative scheme and an effective technique for selecting initial points. The iterative scheme is based on the semi-implicit Euler method, which has both fast and global convergence, and only a small number of initial points is sufficient to detect all unstable periodic orbits of a given period. The power of our method is illustrated by numerical examples of both two- and four-dimensional maps.

chao-dyn↗