Showing papers by "Choy Heng Lai published in 2006"
TL;DR: In this article, the geometric phase of the open two-level system depends only on the smooth (open or closed) curve in the complex projective Hilbert space of ray, which is formulated entirely in terms of geometric structures on this space.
Abstract: A mapping is established in connecting density matrices, associated with an evolution of a quantum open system, with vector ray in a complex projective Hilbert space. By using the corresponding vector ray to represent the open two-level system, we may observe the geometric phase for the open two-level system. The geometric phase of the open two-level system depends only on the smooth (open or closed) curve in the complex projective Hilbert space of ray, which is formulated entirely in terms of geometric structures on this space.
41 citations
TL;DR: A phase-space analysis is developed, which suggests that the effect of noise on generalized chaotic synchronization can be system dependent in that common noise can either induce/enhance or destroy generalized synchronization.
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.
26 citations
TL;DR: In this article, a new geometric phase is proposed by considering both energy and momentum conservation, where the corresponding dynamical phases have two parts differently from the conventional calculations for the phase.
19 citations
TL;DR: In this article, the authors argue 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.
18 citations
TL;DR: It is found that, for a finite-capacity network, perturbations can cause the network to oscillate persistently in the sense that the characterizing quantities vary periodically or randomly with time.
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 quantities respond to sudden changes caused by attacks or disturbances in recoverable networks, i.e., functions of the affected nodes are only temporarily disabled or partially limited. By introducing a model to address this issue, we find that, for a finite-capacity network, perturbations can cause the network to 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.
14 citations
TL;DR: Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers, and the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution.
Abstract: Strange nonchaotic attractors (SNAs) were previously thought to arise exclusively in quasiperiodic dynamical systems. A recent study has revealed, however, that such attractors can be induced by noise in nonquasiperiodic discrete-time maps or in periodically driven flows. In particular, in a periodic window of such a system where a periodic attractor coexists with a chaotic saddle (nonattracting chaotic invariant set), none of the Lyapunov exponents of the asymptotic attractor is positive. Small random noise is incapable of causing characteristic changes in the Lyapunov spectrum, but it can make the attractor geometrically strange by dynamically connecting the original periodic attractor with the chaotic saddle. Here we present a detailed study of noise-induced SNAs and the characterization of their properties. Numerical calculations reveal that the fractal dimensions of noise-induced SNAs typically assume fractional values, in contrast to SNAs in quasiperiodically driven systems whose dimensions are integers. An interesting finding is that the fluctuations of the finite-time Lyapunov exponents away from their asymptotic values obey an exponential distribution, the generality of which we are able to establish by a theoretical analysis using random matrices. We suggest a possible experimental test. We expect noise-induced SNAs to be general.
14 citations
TL;DR: This work shows that by choosing appropriate coupling strategies, CS can be observed in coupled chaotic systems with parameter mismatch, and GS can also be achieved in coupled identical systems.
Abstract: Usually, complete synchronization (CS) is regarded as the form of synchronization proper of identical chaotic systems, while generalized synchronization (GS) extends CS in nonidentical systems. However, this generally accepted view ignores the role that the coupling plays in determining the type of synchronization. In this work, we show that by choosing appropriate coupling strategies, CS can be observed in coupled chaotic systems with parameter mismatch, and GS can also be achieved in coupled identical systems. Numerical examples are provided to demonstrate these findings. Moreover, experimental verification based on electronic circuits has been carried out to support the numerical results. Our work provides a method to obtain robust CS in synchronization-based chaos communications.
14 citations
TL;DR: A phenomenon is found: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value.
Abstract: Resonant perturbations are effective for harnessing nonlinear oscillators for various applications such as controlling chaos and inducing chaos. Of physical interest is the effect of small frequency mismatch on the attractors of the underlying dynamical systems. By utilizing a prototype of nonlinear oscillators, the periodically forced Duffing oscillator and its variant, we find a phenomenon: resonant-frequency mismatch can result in attractors that are nonchaotic but are apparently strange in the sense that they possess a negative Lyapunov exponent but its information dimension measured using finite numerics assumes a fractional value. We call such attractors pseudo-strange. The transition to pesudo-strange attractors as a system parameter changes can be understood analytically by regarding the system as nonstationary and using the Melnikov function. Our results imply that pseudo-strange attractors are common in nonstationary dynamical systems.
8 citations
TL;DR: In this paper, the controllability of chaos in wavelet subspaces has been analyzed and it is shown that depending on the scale of the wavelet operation and the number of the coupled oscillators, the critical coupling strength for the occurrence of chaos synchronization becomes many times smaller if the original coupling matrix is appropriately treated with the Wavelet transform.
Abstract: In this paper, we provide mathematical analysis for the controllability of chaos in wavelet subspaces. We prove that depending on the scale of the wavelet operation and the number of the coupled oscillators, the critical coupling strength for the occurrence of chaos synchronization becomes many times smaller if the original coupling matrix is appropriately treated with the wavelet transform. Moreover, we obtain rigorous relations connecting the critical values and the wavelet subspace operations. Our mathematical results are completely consistent with early numerical simulations.
7 citations
TL;DR: A code generator is designed based on a one-way coupled map lattice (OCML) system, and application of the generated binary spatiotemporal chaotic sequences on baseband spread spectrum communication...
Abstract: A code generator is designed based on a one-way coupled map lattice (OCML) system, and application of the generated binary spatiotemporal chaotic sequences on baseband spread spectrum communication...
4 citations
TL;DR: In this paper, a transition from generalized marginal synchronization to frequency locking in chaotic Rossler oscillators with a non-chaotic attractor was studied and the bifurcation of the dynamical system was investigated.
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TL;DR: This work proposes 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.
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, ie 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