ScholarBank@NUShttps://scholarbank.nus.edu.sgThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Sun, 20 Oct 2019 11:37:20 GMT2019-10-20T11:37:20Z50281- Resonance effect of direction-phase clusters in a scale-free networkhttps://scholarbank.nus.edu.sg/handle/10635/115266Title: Resonance effect of direction-phase clusters in a scale-free network
Authors: Zhou, Y.; Zhou, J.; Wang, X.; Guan, S.; Lai, C.H.; Liu, Z.
Abstract: It is known that for chaotic flows, a weak coupling does not always make the coupled systems approach synchronization but sometimes makes them become more complicated (Phys. Rev. E, 67 (2003) 045203(R)). We here report that a similar situation also occurs in the coupled chaotic maps, where a weak coupling will make the number of direction-phase clusters Nc increase. We find a double-resonance effect on the coupling strength ε, where the first resonance comes from the coupling-induced periodic behaviors and the second one is due to the disappearance of the disorder phase. The mechanism of the second resonance is revealed through the out-of-phase links. Moreover, we show that the critical coupling εc of the maximum Nc will increase rapidly with the bifurcation parameter μ but slowly with the range of the distribution of non-identical oscillators. Copyright © EPLA, 2010.
Fri, 01 Jan 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152662010-01-01T00:00:00Z
- Synchronization stability of general complex dynamical networks with time-varying delayshttps://scholarbank.nus.edu.sg/handle/10635/115963Title: Synchronization stability of general complex dynamical networks with time-varying delays
Authors: Li, K.; Guan, S.; Gong, X.; Lai, C.-H.
Abstract: The synchronization problem of some general complex dynamical networks with time-varying delays is investigated. Both time-varying delays in the network couplings and time-varying delays in the dynamical nodes are considered. The novel delay-dependent criteria in terms of linear matrix inequalities (LMI) are derived based on free-weighting matrices technique and appropriate Lyapunov functional proposed recently. Numerical examples are given to illustrate the effectiveness and advantage of the proposed synchronization criteria. © 2008 Elsevier B.V. All rights reserved.
Mon, 08 Dec 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159632008-12-08T00:00:00Z
- The development of generalized synchronization on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/115980Title: The development of generalized synchronization on complex networks
Authors: Guan, S.; Wang, X.; Gong, X.; Li, K.; Lai, C.-H.
Abstract: In this paper, we numerically investigate the development of generalized synchronization (GS) on typical complex networks, such as scale-free networks, small-world networks, random networks, and modular networks. By adopting the auxiliary-system approach to networks, we observe that GS generally takes place in oscillator networks with both heterogeneous and homogeneous degree distributions, regardless of whether the coupled chaotic oscillators are identical or nonidentical. We show that several factors, such as the network topology, the local dynamics, and the specific coupling strategies, can affect the development of GS on complex networks. © 2009 American Institute of Physics.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159802009-01-01T00:00:00Z
- Understanding synchronization induced by "common noise"https://scholarbank.nus.edu.sg/handle/10635/53249Title: Understanding synchronization induced by "common noise"
Authors: Guan, S.; Lai, Y.-C.; Lai, C.-H.; Gong, X.
Abstract: Noise-induced synchronization refers to the phenomenon where two uncoupled, independent nonlinear oscillators can achieve synchronization through a "common" noisy forcing. Here, "common" means identical. However, "common noise" is a construct which does not exist in practice. Noise by nature is unique and two noise signals cannot be exactly the same. How to justify and understand this central concept in noise-induced synchronization? What is the relation between noise-induced synchronization and the usual chaotic synchronization? Here we argue and demonstrate that noise-induced synchronization is closely related to generalized synchronization as characterized by the emergence of a functional relation between distinct dynamical systems through mutual interaction. We show that the same mechanism applies to the phenomenon of noise-induced (or chaos-induced) phase synchronization.
Mon, 17 Apr 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/532492006-04-17T00:00:00Z
- Characterizing generalized synchronization in complex networkshttps://scholarbank.nus.edu.sg/handle/10635/115638Title: Characterizing generalized synchronization in complex networks
Authors: Guan, S.; Gong, X.; Li, K.; Liu, Z.; Lai, C.-H.
Abstract: Recently, it was shown that generalized synchronization (GS) can generally occur in systems of networked oscillators. In this paper, we further characterize the states of GS by both theoretical analysis and numerical experiments. We show that the entrainment of local dynamics in a network can be characterized by the conditional Lyapunov exponent of the local oscillator. Meanwhile, different types of states of GS can be identified by analyzing the Lyapunov exponent spectra of the coupled system. Most importantly, we further provide direct evidence demonstrating that node dynamics in a network in a chaotic GS state can indeed achieve functional relations, although they may not directly connect to each other in typical complex networks. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Fri, 30 Jul 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1156382010-07-30T00:00:00Z
- Geometry and boundary control of pattern formation and competitionhttps://scholarbank.nus.edu.sg/handle/10635/96724Title: Geometry and boundary control of pattern formation and competition
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: This paper presents the effective control of the formation and competition of cellular patterns. Simulation and theoretical analyses are carried out for pattern formation in a confined circular domain. The Cahn-Hilliard equation is solved with the zero-flux boundary condition to describe the phase separation of binary mixtures. A wavelet-based discrete singular convolution algorithm is employed to provide high-precision numerical solutions. By extensive numerical experiments, a set of cellular ordered state patterns are generated. Theoretical analysis is carried out by using the Fourier-Bessel series. Modal decomposition shows that the pattern morphology of an ordered state pattern is dominated by a principal Fourier-Bessel mode, which has the largest Fourier-Bessel decomposition amplitude. Interesting modal competition is also observed. It is found that the formation and competition of cellular patterns are effectively controlled by the confined geometry and boundary condition. © 2002 Elsevier Science B.V. All rights reserved.
Sat, 15 Feb 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/967242003-02-15T00:00:00Z
- Characterizing the spatiotemporal dynamics of turbulencehttps://scholarbank.nus.edu.sg/handle/10635/95973Title: Characterizing the spatiotemporal dynamics of turbulence
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: This paper introduces a new wavelet-based approach for characterizing the dynamics of turbulence. The proposed approach reduces the dynamics of turbulence into a number of time series, each at a different spatial scale. The effectiveness of the proposed method is illustrated by freely decaying two-dimensional turbulence, which shows three distinct dynamic stages in the present wavelet representation. Increase of the wavelet energies in the large scale subbands characterizes the inverse energy transfer. Moreover, an anomalous transfer of the subband energy and enstrophy among spatial scales is observed during the transient stage. The decaying of the subscale enstrophies exhibits power law scaling and, interestingly, the decay rates increase monotonically with the refinement of the scales. © 2003 Elsevier B.V. All rights reserved.
Wed, 01 Oct 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/959732003-10-01T00:00:00Z
- Controllability of flow turbulencehttps://scholarbank.nus.edu.sg/handle/10635/111355Title: Controllability of flow turbulence
Authors: Guan, S.; Wei, G.W.; Lai, C.-H.
Abstract: The controllability of real-world flow turbulence governed by two-dimensional Navier-Stokes equations, was theoretically investigated using strategies developed in the domain of chaos control. The control of flow turbulence to a spatially periodic pattern, was considered. The control was characterized in terms of control error versus time and the time-averaged control error versus the coupling strength. The results provide an example of controllability of flow turbulence which demonstrates different characteristics from many other distributed systems.
Tue, 01 Jun 2004 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1113552004-06-01T00:00:00Z
- Transition to global synchronization in clustered networkshttps://scholarbank.nus.edu.sg/handle/10635/116009Title: Transition to global synchronization in clustered networks
Authors: Guan, S.; Wang, X.; Lai, Y.-C.; Lai, C.-H.
Abstract: A clustered network is characterized by a number of distinct sparsely linked subnetworks (clusters), each with dense internal connections. Such networks are relevant to biological, social, and certain technological networked systems. For a clustered network the occurrence of global synchronization, in which nodes from different clusters are synchronized, is of interest. We consider Kuramoto-type dynamics and obtain an analytic formula relating the critical coupling strength required for global synchronization to the probabilities of intracluster and intercluster connections, and provide numerical verification. Our work also provides direct support for a previous spectral-analysis-based result concerning the role of random intercluster links in enhancing the synchronizability of a clustered network. © 2008 The American Physical Society.
Tue, 15 Apr 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1160092008-04-15T00:00:00Z
- The many faces of synchronization of networkshttps://scholarbank.nus.edu.sg/handle/10635/115990Title: The many faces of synchronization of networks
Authors: Guan, S.; Wang, X.; Li, K.; Lai, C.-H.
Abstract: Currently, synchronizability of networks is mainly studied in terms of the eigen ratio of the coupling matrix, which is a pure property of network topology. In this work, we clarify that although the eigen ratio is relevant to the possible range of coupling strength for achieving synchronization, it cannot fully determine the latter. The magnitude of the eigenvalues also plays a decisive role. We emphasize that synchronizability of networks is inherently related to the local dynamics on networks. It is not appropriate to discuss synchronizability of networks without considering the specific dynamics on them. For three typical types of local dynamics, we discuss the implication of synchronizability of networks. © 2009 World Scientific Publishing Company.
Tue, 30 Jun 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159902009-06-30T00:00:00Z
- Transition to amplitude death in scale-free networkshttps://scholarbank.nus.edu.sg/handle/10635/115336Title: Transition to amplitude death in scale-free networks
Authors: Liu, W.; Wang, X.; Guan, S.; Lai, C.-H.
Abstract: Transition to amplitude death in scale-free networks of nonlinear oscillators is investigated both numerically and analytically. It is found that, as the coupling strength increases, the network will undergo three different stages in approaching the state of complete amplitude death (CAD). In the first stage of the transition, the amplitudes of the oscillators present a 'stair-like' arrangement, i.e. the squared amplitude of an oscillator linearly decreases with the number of links that the oscillator receives (node degree). In this stage, as the coupling strength increases, the amplitude stairs are eliminated hierarchically by descending order of the node degree. At the end of the first stage, except for a few synchronized oscillators, all other oscillators in the network have small amplitudes. Then, in the second stage of the transition, the synchronous clusters formed in the first stage gradually disappear and, as a consequence, the number of small-amplitude oscillators is increased. At the end of the second stage, almost all oscillators in the network have small but finite amplitudes. Finally, in the third stage of the transition, without the support of the synchronous clusters, the amplitudes of the oscillators are quickly decreased, eventually leading to the state of CAD. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Tue, 15 Sep 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1153362009-09-15T00:00:00Z
- Disorder effect on electronic and optical properties of doped carbon nanotubeshttps://scholarbank.nus.edu.sg/handle/10635/115678Title: Disorder effect on electronic and optical properties of doped carbon nanotubes
Authors: Ma, J.; Guan, S.; Lai, C.-H.
Abstract: In this work, we investigate the effects of disorder in the doped carbon nanotubes. Based on the extended Su-Schrieffer-Heeger model, it is shown that with the increase of doped impurity atoms, such as nitrogen or boron, the symmetry of the hopping processes among the doped and carbon lattices collapses, and the statistics of the nearest neighbor energy level spacing changes from the Poisson distribution to the Wigner distribution, indicating the occurrence of disorder effect in heavily doped nanotubes. As a result, the nanotube changes from a metal to a semiconductor. We also study the disorder effect on linear optical absorption in doped nanotubes. It is demonstrated that the linear optical absorption can be greatly suppressed due to the collapse of the discrete spatial symmetry in heavily doped nanotubes. Based on the random matrix theory, we carry out a theoretical analysis, which agrees well with our numerical simulations. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1156782006-01-01T00:00:00Z
- Spontaneous formation of dynamical groups in an adaptive networked systemhttps://scholarbank.nus.edu.sg/handle/10635/115294Title: Spontaneous formation of dynamical groups in an adaptive networked system
Authors: Li, M.; Guan, S.; Lai, C.-H.
Abstract: In this work, we investigate a model of an adaptive networked dynamical system, where the coupling strengths among phase oscillators coevolve with the phase states. It is shown that in this model the oscillators can spontaneously differentiate into two dynamical groups after a long time evolution. Within each group, the oscillators have similar phases, while oscillators in different groups have approximately opposite phases. The network gradually converts from the initial random structure with a uniform distribution of connection strengths into a modular structure that is characterized by strong intra-connections and weak inter-connections. Furthermore, the connection strengths follow a power-law distribution, which is a natural consequence of the coevolution of the network and the dynamics. Interestingly, it is found that if the inter-connections are weaker than a certain threshold, the two dynamical groups will almost decouple and evolve independently. These results are helpful in further understanding the empirical observations in many social and biological networks. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Tue, 19 Oct 2010 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152942010-10-19T00:00:00Z
- Effect of noise on generalized chaotic synchronizationhttps://scholarbank.nus.edu.sg/handle/10635/111375Title: Effect of noise on generalized chaotic synchronization
Authors: Guan, S.; Lai, Y.-C.; Lai, C.-H.
Abstract: When two characteristically different chaotic oscillators are coupled, generalized synchronization can occur. Motivated by the phenomena that common noise can induce and enhance complete synchronization or phase synchronization in chaotic systems, we investigate the effect of noise on generalized chaotic synchronization. We develop a phase-space analysis, which suggests that the effect can be system dependent in that common noise can either induce/enhance or destroy generalized synchronization. A prototype model consisting of a Lorenz oscillator coupled with a dynamo system is used to illustrate these phenomena. © 2006 The American Physical Society.
Sun, 01 Jan 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1113752006-01-01T00:00:00Z
- Frequency locking by external force from a dynamical system with strange nonchaotic attractorhttps://scholarbank.nus.edu.sg/handle/10635/115118Title: Frequency locking by external force from a dynamical system with strange nonchaotic attractor
Authors: Guan, S.; Wang, X.; Lai, C.-H.
Abstract: Usually, phase synchronization is studied in chaotic systems driven by either periodic force or chaotic force. In the present work, we consider frequency locking in chaotic Rössler oscillator by a special driving force from a dynamical system with a strange nonchaotic attractor. In this case, a transition from generalized marginal synchronization to frequency locking is observed. We investigate the bifurcation of the dynamical system and explain why generalized marginal synchronization can occur in this model. © 2006 Elsevier B.V. All rights reserved.
Mon, 05 Jun 2006 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1151182006-06-05T00:00:00Z
- Controlling flow turbulencehttps://scholarbank.nus.edu.sg/handle/10635/96097Title: Controlling flow turbulence
Authors: Guan, S.; Zhou, Y.C.; Wei, G.W.; Lai, C.-H.
Abstract: This paper investigates the viability and effectiveness of using a technique developed for low-dimensional chaotic systems to control flow turbulence governed by the Navier-Stokes equations. By using a global pinning coupling strategy, we show that turbulence can be controlled to desirable time-varying target states, including a spatially extended periodic state and a turbulent one. Exponential convergence to the target state is found and the exponential rate scales linearly to the coupling strength. The linear scaling law breaks down when localized pinning control is applied. A wavelet multiscale technique is utilized for the characterization of both the effectiveness of the present control strategy and the inverse energy transfer in two-dimensional turbulence. © 2003 American Institute of Physics.
Sat, 01 Mar 2003 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/960972003-03-01T00:00:00Z
- Dynamical formation of stable irregular transients in discontinuous map systemshttps://scholarbank.nus.edu.sg/handle/10635/115683Title: Dynamical formation of stable irregular transients in discontinuous map systems
Authors: Zou, H.; Guan, S.; Lai, C.-H.
Abstract: Stable chaos refers to the long irregular transients, with a negative largest Lyapunov exponent, which is usually observed in certain high-dimensional dynamical systems. The mechanism underlying this phenomenon has not been well studied so far. In this paper, we investigate the dynamical formation of stable irregular transients in coupled discontinuous map systems. Interestingly, it is found that the transient dynamics has a hidden pattern in the phase space: it repeatedly approaches a basin boundary and then jumps from the boundary to a remote region in the phase space. This pattern can be clearly visualized by measuring the distance sequences between the trajectory and the basin boundary. The dynamical formation of stable chaos originates from the intersection points of the discontinuous boundaries and their images. We carry out numerical experiments to verify this mechanism. © 2009 The American Physical Society.
Fri, 23 Oct 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1156832009-10-23T00:00:00Z
- Phase synchronization between two essentially different chaotic systemshttps://scholarbank.nus.edu.sg/handle/10635/115230Title: Phase synchronization between two essentially different chaotic systems
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: In this paper, we numerically investigate phase synchronization between two coupled essentially different chaotic oscillators in drive-response configuration. It is shown that phase synchronization can be observed between two coupled systems despite the difference and the large frequency detuning between them. Moreover, the relation between phase synchronization and generalized synchronization is compared with that in coupled parametrically different systems. In the systems studied, it is found that phase synchronization occurs after generalized synchronization in coupled essentially different chaotic systems. © 2005 The American Physical Society.
Fri, 01 Jul 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1152302005-07-01T00:00:00Z
- Onset of synchronization in complex gradient networkshttps://scholarbank.nus.edu.sg/handle/10635/115847Title: Onset of synchronization in complex gradient networks
Authors: Wang, X.; Huang, L.; Guan, S.; Lai, Y.-C.; Lai, C.H.
Abstract: Recently, it has been found that the synchronizability of a scale-free network can be enhanced by introducing some proper gradient in the coupling. This result has been obtained by using eigenvalue-spectrum analysis under the assumption of identical node dynamics. Here we obtain an analytic formula for the onset of synchronization by incorporating the Kuramoto model on gradient scale-free networks. Our result provides quantitative support for the enhancement of synchronization in such networks, further justifying their ubiquity in natural and in technological systems. © 2008 American Institute of Physics.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1158472008-01-01T00:00:00Z
- Synchronizability of network ensembles with prescribed statistical propertieshttps://scholarbank.nus.edu.sg/handle/10635/115962Title: Synchronizability of network ensembles with prescribed statistical properties
Authors: Guan, S.; Wang, X.; Li, K.; Wang, B.-H.; Lai, C.-H.
Abstract: 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. © 2008 American Institute of Physics.
Tue, 01 Jan 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159622008-01-01T00:00:00Z
- Controlling flow turbulence with moving controllershttps://scholarbank.nus.edu.sg/handle/10635/115044Title: Controlling flow turbulence with moving controllers
Authors: Tang, G.; Guan, S.; Hu, G.
Abstract: In this work, we consider how to improve the efficiency of controlling flow turbulence in two-dimensional Navier-Stokes equations. We suggest a control strategy which applies local feedback injections by moving controllers. In the moving frame, this strategy is equivalent to adding a gradient force term in the governing equation. It is shown that with the moving controllers, flow turbulence can be controlled more efficient than the usual pinning strategy with static controllers, provided that the number of controllers and the injection energy are the same. The physical mechanism underlying this higher control efficiency is heuristically analyzed. The advantages and difficulties of the proposed control strategy in practical applications are discussed.
Tue, 01 Nov 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1150442005-11-01T00:00:00Z
- Desynchronization and on-off intermittency in complex networkshttps://scholarbank.nus.edu.sg/handle/10635/111360Title: Desynchronization and on-off intermittency in complex networks
Authors: Wang, X.; Guan, S.; Lai, Y.-C.; Li, B.; Lai, C.H.
Abstract: Most existing works on synchronization in complex networks concern the synchronizability and its dependence on network topology. While there has also been work on desynchronization wave patterns in networks that are regular or nearly regular, little is known about the dynamics of synchronous patterns in complex networks. We find that, when a complex network becomes desynchronized, a giant cluster of a vast majority of synchronous nodes can form. A striking phenomenon is that the size of the giant cluster can exhibit an extreme type of intermittent behavior: on-off intermittency. We articulate a physical theory to explain this behavior. This phenomenon may have implications to the evolution of real-world systems. Copyright © 2009 EPLA.
Thu, 01 Jan 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1113602009-01-01T00:00:00Z
- Protecting infrastructure networks from cost-based attackshttps://scholarbank.nus.edu.sg/handle/10635/115890Title: Protecting infrastructure networks from cost-based attacks
Authors: Wang, X.; Guan, S.; Lai, C.H.
Abstract: It is well known that heterogeneous networks are vulnerable to the intentional removal of a small fraction of highly connected or loaded nodes, implying that to protect the network effectively, the important nodes should be allocated more defense resource than the others. However, if too much resource is allocated to the few important nodes, the numerous less-important nodes will be less protected, which if attacked together can still lead to devastating damage. A natural question is therefore how to efficiently distribute the limited defense resource among the network nodes such that the network damage is minimized against any attack strategy. In this paper, taking into account the factor of attack cost, the problem of network security is reconsidered in terms of efficient network defense against cost-based attacks. The results show that, for a general complex network, there exists an optimal distribution of the defense resource with which the network is best protected from cost-based attacks. Furthermore, it is found that the configuration of the optimal defense is dependent on the network parameters. Specifically, networks of larger size, sparser connection and more heterogeneous structure will more likely benefit from the defense optimization. © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.
Tue, 03 Mar 2009 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1158902009-03-03T00:00:00Z
- Stability of the steady state of delay-coupled chaotic maps on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/115946Title: Stability of the steady state of delay-coupled chaotic maps on complex networks
Authors: Gong, X.; Guan, S.; Wang, X.; Lai, C.-H.
Abstract: We study the stability of the steady state of coupled chaotic maps with randomly distributed time delays evolving on a random network. An analysis method is developed based on the peculiar mathematical structure of the Jacobian of the steady state due to time-delayed coupling, which enables us to relate the stability of the steady state to the locations of the roots of a set of lower-order bound equations. For δ -distributed time delays (or fixed time delay), we find that the stability of the steady state is determined by the maximum modulus of the roots of a set of algebraic equations, where the only nontrivial coefficient in each equation is one of the eigenvalues of the normalized adjacency matrix of the underlying network. For general distributed time delays, we find a necessary condition for the stable steady state based on the maximum modulus of the roots of a bound equation. When the number of links is large, the nontrivial coefficients of the bound equation are just the probabilities of different time delays. Our study thus establishes the relationship between the stability of the steady state and the probability distribution of time delays, and provides a better way to investigate the influence of the distributed time delays in coupling on the global behavior of the systems. © 2008 The American Physical Society.
Tue, 20 May 2008 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1159462008-05-20T00:00:00Z
- Bistable chaos without symmetry in generalized synchronizationhttps://scholarbank.nus.edu.sg/handle/10635/115613Title: Bistable chaos without symmetry in generalized synchronization
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: Frequently, multistable chaos is found in dynamical systems with symmetry. We demonstrate a rare example of bistable chaos in generalized synchronization (GS) in coupled chaotic systems without symmetry. Bistable chaos in GS refers to two chaotic attractors in the response system which both synchronize with the driving dynamics in the sense of GS. By choosing appropriate coupling, the coupled system could be symmetric or asymmetric. Interestingly, it is found that the response system exhibits bistability in both cases. Three different types of bistable chaos have been identified. The crisis bifurcations which lead to the bistability are explored, and the relation between the bistable attractors is analyzed. The basin of attraction of the bistable attractors is extensively studied in both parameter space and initial condition space. The fractal basin boundary and the riddled basin are observed and they are characterized in terms of the uncertainty exponent. ©2005 The American Physical Society.
Tue, 01 Mar 2005 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1156132005-03-01T00:00:00Z
- Fourier-Bessel analysis of patterns in a circular domainhttps://scholarbank.nus.edu.sg/handle/10635/96671Title: Fourier-Bessel analysis of patterns in a circular domain
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: This paper explores the use of the Fourier-Bessel analysis for characterizing patterns in a circular domain. A set of stable patterns is found to be well-characterized by the Fourier-Bessel functions. Most patterns are dominated by a principal Fourier-Bessel mode [n, m] which has the largest Fourier-Bessel decomposition amplitude when the control parameter R is close to a corresponding non-trivial root (ρn,m) of the Bessel function. Moreover, when the control parameter is chosen to be close to two or more roots of the Bessel function, the corresponding principal Fourier-Bessel modes compete to dominate the morphology of the patterns. © 2001 Elsevier Science B.V.
Tue, 01 May 2001 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/966712001-05-01T00:00:00Z
- Analysis of traffic flow on complex networkshttps://scholarbank.nus.edu.sg/handle/10635/114996Title: Analysis of traffic flow on complex networks
Authors: Li, K.; Gong, X.; Guan, S.; Lai, C.-H.
Abstract: We propose a new routing strategy for controlling packet routing on complex networks. The delivery capability of each node is adopted as a piece of local information to be integrated with the load traffic dynamics to weight the next route. The efficiency of transport on complex network is measured by the network capacity, which is enhanced by distributing the traffic load over the whole network while nodes with high handling ability bear relative heavier traffic burden. By avoiding the packets through hubs and selecting next routes optimally, most travel times become shorter. The simulation results show that the new strategy is not only effective for scale-free networks but also for mixed networks in realistic networks. © 2011 World Scientific Publishing Company.
Wed, 20 Apr 2011 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/1149962011-04-20T00:00:00Z
- A wavelet method for the characterization of spatiotemporal patternshttps://scholarbank.nus.edu.sg/handle/10635/95703Title: A wavelet method for the characterization of spatiotemporal patterns
Authors: Guan, S.; Lai, C.-H.; Wei, G.W.
Abstract: This paper introduces a wavelet-based method for the characterization of spatiotemporal patterns. Based on the wavelet multiresolution analysis, two wavelet indices, multiscale accumulative density (MAD) and multiscale accumulative change (MAC), are proposed for the characterization of the dynamics of the spatiotemporal patterns. Both indices are constructed by using orthogonal wavelet projection operators. The MAD is a measure of the spatial complexity of a pattern at a given time, whereas the MAC characterizes the spatial complexity of instantaneous change of the spatiotemporal patterns at a given time. The ratio of the MAD indices between the lowest and the highest scales reflects the order of coherence in a pattern. The time series of both MAD and MAC provide the dynamical information of morphological pattern evolutions. Numerical experiments based on the Cahn-Hilliard equation indicate that the proposed method is efficient for quantitatively characterizing the dynamics of the spatiotemporal patterns. © 2002 Published by Elsevier Science B.V.
Fri, 01 Mar 2002 00:00:00 GMThttps://scholarbank.nus.edu.sg/handle/10635/957032002-03-01T00:00:00Z