Biomedical subjects

Ying-Cheng Lai

Publications and source records attributed to Ying-Cheng Lai.

At least 19 recordsLinked to original sources

PubMed2006

Abnormal synchronization in complex clustered networks.

Recent research has revealed that complex networks with a smaller average distance and more homogeneous degree distribution are more synchronizable. We find, however, that synchronization in complex, clustered networks tends to obey a different set of rules. In particular, the synchronizability of such a network is determined by the interplay between intercluster and intracluster links. The network is most synchronizable when the numbers of the two types of links are approximately equal. In the presence of a mismatch, increasing the number of intracluster links, while making the network distance smaller, can counterintuitively suppress or even destroy the synchronization. We provide theory and numerical evidence to establish this phenomenon.

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PubMed2006

Characterization of noise-induced strange nonchaotic attractors.

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.

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PubMed2006

Percolation and blind spots in complex networks.

Recent works on network security have focused on whether a complex network can maintain its integrability under attack or random node failures. In applications of increasing importance such as sensor networks, a somewhat different problem, namely, the occurrence of isolated nodes (or blind spots), is of great interest. We show that, for networks with a stronger ability to form global spanning clusters, it is relatively more difficult to eliminate blind spots, and vice versa. We use the framework of percolation to investigate this phenomenon. Our analysis also yields a formula for the average number of blind spots, which provide an explanation for several numerical findings.

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PubMed2006

Effect of noise on generalized chaotic synchronization.

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.

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PubMed2006

Information propagation on modular networks.

Networks with a community (or modular) structure underlie many social and biological phenomena. In such a network individuals tend to form sparsely linked local communities, each having dense internal connections. We investigate the dynamics of information propagation on modular networks by using a three-state epidemic model with a unit spreading rate (i.e., the probability for a susceptible individual to be "infected" with the information is one). We find a surprising, resonancelike phenomenon: the information lifetime on the network can be maximized by the number of modules. The result can be useful for optimizing or controlling information spread on social or biological networks.

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PubMed2006

Detecting and characterizing phase synchronization in nonstationary dynamical systems.

We propose a general framework for detecting and characterizing phase synchronization from noisy, nonstationary time series. For detection, we propose to use the average phase-synchronization time and show that it is extremely sensitive to parameter changes near the onset of phase synchronization. To characterize the degree of temporal phase synchronization, we suggest to monitor the evolution of phase diffusion from a moving time window and argue that this measure is practically useful as it can be enhanced by increasing the size of the window. While desynchronization events can be caused by either a lack of sufficient deterministic coupling or noise, we demonstrate that the time scales associated with the two mechanisms are quite different. In particular, noise-induced desynchronization events tend to occur on much shorter time scales. This allows for the effect of noise on phase synchronization to be corrected in a practically doable manner. We perform a control study to substantiate these findings by constructing and investigating a prototype model of nonstationary dynamical system that consists of coupled chaotic oscillators with time-varying coupling parameter.

Algorithms↗

PubMed2006

Synchronization in complex networks with a modular structure.

Networks with a community (or modular) structure arise in social and biological sciences. In such a network individuals tend to form local communities, each having dense internal connections. The linkage among the communities is, however, much more sparse. The dynamics on modular networks, for instance synchronization, may be of great social or biological interest. (Here by synchronization we mean some synchronous behavior among the nodes in the network, not, for example, partially synchronous behavior in the network or the synchronizability of the network with some external dynamics.) By using a recent theoretical framework, the master-stability approach originally introduced by Pecora and Carroll in the context of synchronization in coupled nonlinear oscillators, we address synchronization in complex modular networks. We use a prototype model and develop scaling relations for the network synchronizability with respect to variations of some key network structural parameters. Our results indicate that random, long-range links among distant modules is the key to synchronization. As an application we suggest a viable strategy to achieve synchronous behavior in social networks.

Action Potentials↗

PubMed2006

Basin topology in dissipative chaotic scattering.

Chaotic scattering in open Hamiltonian systems under weak dissipation is not only of fundamental interest but also important for problems of current concern such as the advection and transport of inertial particles in fluid flows. Previous work using discrete maps demonstrated that nonhyperbolic chaotic scattering is structurally unstable in the sense that the algebraic decay of scattering particles immediately becomes exponential in the presence of weak dissipation. Here we extend the result to continuous-time Hamiltonian systems by using the Henon-Heiles system as a prototype model. More importantly, we go beyond to investigate the basin structure of scattering dynamics. A surprising finding is that, in the common case where multiple destinations exist for scattering trajectories, Wada basin boundaries are common and they appear to be structurally stable under weak dissipation, even when other characteristics of the nonhyperbolic scattering dynamics are not. We provide numerical evidence and a geometric theory for the structural stability of the complex basin topology.

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PubMed2006

Cooperation of spike timing-dependent and heterosynaptic plasticities in neural networks: a Fokker-Planck approach.

It is believed that both Hebbian and homeostatic mechanisms are essential in neural learning. While Hebbian plasticity selectively modifies synaptic connectivity according to activity experienced, homeostatic plasticity constrains this change so that neural activity is always within reasonable physiological limits. Recent experiments reveal spike timing-dependent plasticity (STDP) as a new type of Hebbian learning with high time precision and heterosynaptic plasticity (HSP) as a new homeostatic mechanism acting directly on synapses. Here, we study the effect of STDP and HSP on randomly connected neural networks. Despite the reported successes of STDP to account for neural activities at the single-cell level, we find that, surprisingly, at the network level, networks trained using STDP alone cannot seem to generate realistic neural activities. For instance, STDP would stipulate that past sensory experience be maintained forever if it is no longer activated. To overcome this difficulty, motivated by the fact that HSP can induce strong competition between sensory experiences, we propose a biophysically plausible learning rule by combining STDP and HSP. Based on the Fokker-Planck theory and extensive numerical computations, we demonstrate that HSP and STDP operated on different time scales can complement each other, resulting in more realistic network activities. Our finding may provide fresh insight into the learning mechanism of the brain.

Action Potentials↗

PubMed2006

Effect of resonant-frequency mismatch on attractors.

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.

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PubMed2005

Beneficial role of noise in promoting species diversity through stochastic resonance.

There is an increasing recognition that patterns in species diversity cannot be understood without reference to nonequilibrial or unstable dynamics. Recently, through a realistic ecological model that involves dispersal, we have addressed the positive role of noise in promoting species coexistence [Phys. Rev. Lett. 94, 038102 (2005)]. Here we present a physical theory to account for the main scaling law responsible for this phenomenon.

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PubMed2005

Transition to intermittent chaotic synchronization.

Coupled chaotic oscillators can exhibit intermittent synchronization in the weakly coupling regime, as characterized by the entrainment of their dynamical variables in random time intervals of finite duration. We find that the transition to intermittent synchronization can be characteristically distinct for geometrically different chaotic attractors. In particular, for coupled phase-coherent chaotic attractors such as those from the Rössler system, the transition occurs immediately as the coupling is increased from zero. For phase-incoherent chaotic attractors such as those in the Lorenz system, the transition occurs only when the coupling is sufficiently strong. A theory based on the behavior of the Lyapunov exponents and unstable periodic orbits is developed to understand these distinct transitions.

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PubMed2005

Tolerance of scale-free networks against attack-induced cascades.

Scale-free networks can be disintegrated by attack on a single or a very few nodes through the process of cascading failures. By utilizing a prototype cascading model, we previously determined the critical value of the capacity parameter below which the network can become disintegrated due to attack on a single node. A fundamental question in network security, which has not been addressed previously but may be more important and of wider interest, is how to design networks of finite capacity that are safe against cascading breakdown. Here we derive an upper bound for the capacity parameter, above which the network is immune to cascading breakdown. Our theory also yields estimates for the maximally achievable network integrity via controlled removal of a small set of low-degree nodes. The theoretical results are confirmed numerically.

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PubMed2005

Self-organized scale-free networks.

Growth and preferential attachments have been coined as the two fundamental mechanisms responsible for the scale-free feature in complex networks, as characterized by an algebraic degree distribution. There are situations, particularly in biological networks, where growth is absent or not important, yet some of these networks still exhibit the scale-free feature with a small degree exponent. Here we propose two classes of models to account for this phenomenon. We show analytically and numerically that, in the first model, a spectrum of algebraic degree distributions with a small exponent can be generated. The second model incorporates weights for nodes, and it is able to generate robust scale-free degree distribution with larger algebraic exponents. Our results imply that it is natural for a complex network to self-organize itself into a scale-free state without growth.

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PubMed2005

Basins of attraction in piecewise smooth Hamiltonian systems.

Piecewise smooth Hamiltonian systems arise in physical and engineering applications. For such a system typically an infinite number of quasi-periodic "attractors" coexist. (Here we use the term "attractors" to indicate invariant sets to which typically initial conditions approach, as a result of the piecewise smoothness of the underlying system. These "attractors" are therefore characteristically different from the attractors in dissipative dynamical systems.) We find that the basins of attraction of different "attractors" exhibit a riddled-like feature in that they mix with each other on arbitrarily fine scales. This practically prevents prediction of "attractors" from specific initial conditions and parameters. The mechanism leading to the complicated basin structure is found to be characteristically different from those reported previously for similar basin structure in smooth dynamical systems. We demonstrate the phenomenon using a class of electronic relaxation oscillators with voltage protection and provide a theoretical explanation.

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PubMed2005

Jamming in complex gradient networks.

Flows of physical quantities in large complex networks, natural or man made, rely in general on some scalar gradients existing in the networks. We investigate, analytically and numerically, under what conditions jamming in gradient flows can occur in random and scale-free networks. We find that the degree of jamming typically increases with the average connectivity of the network. A crossover phenomenon is uncovered where for < k(c) (k(c) denotes a critical connectivity, estimated to be about 10), scale-free networks have a higher level of congestion than random networks with the same , while the opposite occurs for > k(c).

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PubMed2005

Inducing chaos by resonant perturbations: theory and experiment.

We propose a scheme to induce chaos in nonlinear oscillators that either are by themselves incapable of exhibiting chaos or are far away from parameter regions of chaotic behaviors. Our idea is to make use of small, judiciously chosen perturbations in the form of weak periodic signals with time-varying frequency and phase, and to drive the system into a hierarchy of nonlinear resonant states and eventually into chaos. We demonstrate this method by using numerical examples and a laboratory experiment with a Duffing type of electronic circuit driven by a phase-locked loop. The phase-locked loop can track the instantaneous frequency and phase of the Duffing circuit and deliver resonant perturbations to generate robust chaos.

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PubMed2005

Scaling laws for noise-induced super-persistent chaotic transients.

A super-persistent chaotic transient is characterized by the following scaling law for its average lifetime: tau approximately exp[C(p- p(c))(-alpha)] , where C>0 and alpha>0 are constants, p > or = p(c) is a bifurcation parameter, and p(c) is its critical value. As p approaches p(c) from above, the exponent in the exponential dependence diverges, leading to an extremely long transient lifetime. Historically the possibility of such transient raised the question of whether asymptotic attractors are relevant to turbulence. Here we investigate the phenomenon of noise-induced super-persistent chaotic transients. In particular, we construct a prototype model based on random maps to illustrate this phenomenon. We then approximate the model by stochastic differential equations and derive the scaling laws for the transient lifetime versus the noise amplitude epsilon for both the subcritical (p< p(c)) and the supercritical (p> p(c)) cases. Our results are the following. In the subcritical case where a chaotic attractor exists in the absence of noise, noise-induced transients can be more persistent in the following sense of double-exponential and algebraic scaling: tau approximately exp[K0 exp(K1epsilon(-gamma))] for small noise amplitude epsilon, where K0 >0 , K1 >0, and gamma>0 are constants. The longevity of the transient lifetime in this case is striking. For the supercritical case where there is already a super-persistent chaotic transient, noise can significantly reduce the transient lifetime. These results add to the understanding of the interplay between random and deterministic chaotic dynamics with surprising physical implications.

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