Showing papers by "Choy Heng Lai published in 2009"

Transition to amplitude death in scale-free networks

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.

The development of generalized synchronization on complex networks.

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.

Protecting infrastructure networks from cost-based attacks

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.

Desynchronization and on-off intermittency in complex networks

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.

Exploring network structures in feature space

Abstract: We propose a multi-phase approach to explore network structures. In this method, structure analysis is not carried out on the observed network directly. Instead, certain similarity measures of the nodes are derived from the network firstly, which are then projected onto an appropriate lower-dimensional feature space. The clustering structure can be defined in the feature space, and analyzed by conventional clustering algorithms. The classified data are finally mapped back to the original network space if necessary to complete the analysis of network structures. By mapping onto the feature space, some difficulties due to the diversity of micro-structures and scale of the network can be circumvented. This makes it possible for the proposed method to deal with more general structures such as detecting groups in a random background, as well as identifying usual community structures in networks.

One-dimensional hard-point gas as a thermoelectric engine

Abstract: We demonstrate the possibility to build a thermoelectric engine using a one-dimensional gas of molecules with unequal masses and hard-point interaction. Most importantly, we show that the efficiency of this engine is determined by a parameter $YT$ which is different from the well known figure of merit $ZT$. Even though the efficiency of this particular model is low, our results shed light on the problem and open the possibility to build efficient thermoelectric engines.

Evolutionary Subnetworks in Complex Systems

Abstract: Links in a practical network may have different functions, which makes the original network a combination of some functional subnetworks. Here, by a model of coupled oscillators, we investigate how such functional subnetworks are evolved and developed according to the network structure and dynamics. In particular, we study the case of evolutionary clustered networks in which the function of each link (either attractive or repulsive coupling) is updated by the local dynamics. It is found that, during the process of system evolution, the network is gradually stabilized into a particular form in which the attractive (repulsive) subnetwork consists only the intralinks (interlinks). Based on the properties of subnetwork evolution, we also propose a new algorithm for network partition which is distinguished by the convenient operation and fast computing speed.

Dynamical formation of stable irregular transients in discontinuous map systems.

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.

Protecting infrastructure networks from cost-based attacks

Abstract: It has been known that heterogeneous networks are vulnerable to the intentional removal of a small fraction of highly connected or loaded nodes, which implies that, to protect a network effectively, a few important nodes should be allocated with more defense resources than the others. However, if too many resources are allocated to the few important nodes, the numerous less-important nodes will be less protected, which, when attacked all together, still capable of causing a devastating damage. A natural question therefore is how to efficiently distribute the limited defense resources among the network nodes such that the network damage is minimized whatever attack strategy the attacker may take. In this paper, taking into account the factor of attack cost, we will revisit the problem of network security and search for efficient network defense against the cost-based attacks. The study shows that, for a general complex network, there will exist an optimal distribution of the defense resources, with which the network is well protected from cost-based attacks. Furthermore, it is found that the configuration of the optimal defense is dependent on the network parameters. Specifically, network that has a larger size, sparser connection and more heterogeneous structure will be more benefited from the defense optimization.

The many faces of synchronization of networks

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.