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Search Results: 1 - 10 of 48953 matches for " Ying-Cheng Lai "
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Cusp-scaling behavior in fractal dimension of chaotic scattering
Adilson E. Motter,Ying-Cheng Lai
Physics , 2002, DOI: 10.1103/PhysRevE.65.065201
Abstract: 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.
Cascade-based attacks on complex networks
Adilson E. Motter,Ying-Cheng Lai
Physics , 2003, DOI: 10.1103/PhysRevE.66.065102
Abstract: 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.
Efficient algorithm for detecting unstable periodic orbits in chaotic systems
Ruslan L. Davidchack,Ying-Cheng Lai
Physics , 1999, DOI: 10.1103/PhysRevE.60.6172
Abstract: 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.
Oscillations of complex networks
Xingang Wang,Ying-Cheng Lai,Chong Heng Lai
Physics , 2006, DOI: 10.1103/PhysRevE.74.066104
Abstract: 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.
Synchronization in Gradient Networks
Xingang Wang,Ying-Cheng Lai,Choy Heng Lai
Physics , 2006,
Abstract: 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.
Blowout bifurcation of chaotic saddles
Tomasz Kapitaniak,Ying-Cheng Lai,Celso Grebogi
Discrete Dynamics in Nature and Society , 1998, DOI: 10.1155/s1026022699000023
Abstract: Chaotic saddles are nonattracting dynamical invariant sets that can lead to a variety of physical phenomena. We describe the blowout bifurcation of chaotic saddles located in the symmetric invariant manifold of coupled systems and discuss dynamical phenomena associated with this bifurcation.
Range-based attack on links in scale-free networks: are long-range links responsible for the small-world phenomenon?
Adilson E. Motter,Takashi Nishikawa,Ying-Cheng Lai
Physics , 2002, DOI: 10.1103/PhysRevE.66.065103
Abstract: 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.
Large-scale structural organization of social networks
Adilson E. Motter,Takashi Nishikawa,Ying-Cheng Lai
Physics , 2003, DOI: 10.1103/PhysRevE.68.036105
Abstract: 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.
Reactive dynamics of inertial particles in nonhyperbolic chaotic flows
Adilson E. Motter,Ying-Cheng Lai,Celso Grebogi
Physics , 2003, DOI: 10.1103/PhysRevE.68.056307
Abstract: 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.
Transition to turbulence in ferrofluids
Sebastian Altmeyer,Younghae Do,Ying-Cheng Lai
Physics , 2015,
Abstract: It is known that in classical fluids turbulence typically occurs at high Reynolds numbers. But can turbulence occur at low Reynolds numbers? Here we investigate the transition to turbulence in the classic Taylor-Couette system in which the rotating fluids are manufactured ferrofluids with magnetized nanoparticles embedded in liquid carriers. We find that, in the presence of a magnetic field turbulence can occur at Reynolds numbers that are at least one order of magnitude smaller than those in conventional fluids. This is established by extensive computational ferrohydrodynamics through a detailed bifurcation analysis and characterization of behaviors of physical quantities such as the energy, the wave number, and the angular momentum through the bifurcations. A striking finding is that, as the magnetic field is increased, the onset of turbulence can be determined accurately and reliably. Our results imply that experimental investigation of turbulence can be greatly facilitated by using ferrofluids, opening up a new avenue to probe into the fundamentals of turbulence and the challenging problem of turbulence control.
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