Biomedical subjects

Xingang Wang

Publications and source records attributed to Xingang Wang.

9 recordsLinked to original sources

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.

Journal Article↗

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.

Journal Article↗

PubMed2005

Phase synchronization of a pair of spiral waves.

The interaction of a pair of spiral waves with different independent rotation frequencies is studied. In a very large frequency mismatch searching region, we observe three different pattern formation phenomena: (a) phase-synchronization-induced invasion under a relatively small frequency mismatch, i.e., the spiral wave with slower frequency (longer period) is swept away by a traveling wave, which is induced and phase synchronized by the faster spiral wave; (b) the coexistence of two spiral waves at sufficiently large parameter mismatch; and (c) an intermediate state, a non-phase-synchronous invasion, that is, similarly the slower spiral wave is swept by an approximate planar wave, whose frequency, however, is intermediate between those of the faster and slower waves. A point-source model is studied to analyze all these phenomena in a unified way.

Journal Article↗

PubMed2005

Public-key encryption based on generalized synchronization of coupled map lattices.

Currently used public-key cryptosystems are based on difficulties in solving certain numeric theoretic problems, in which the way to predict the private key from the knowledge of the public key is computationally infeasible. Here we propose a method of constructing public-key cryptosystems by generalized synchronization of coupled map lattices, in which the difficulty in predicting the synchronous function is used as the trap-door function to deduce the private key from the public key. In specific, we implement this idea on the method of "Merkle's puzzles," and find that, incorporated with the chaotic dynamics, this traditional method is equipped with some new features and can be practical in certain situations.

Journal Article↗

PubMed2004

Strange nonchaotic attractors in random dynamical systems.

Whether strange nonchaotic attractors (SNAs) can occur typically in dynamical systems other than quasiperiodically driven systems has long been an open question. Here we show, based on a physical analysis and numerical evidence, that robust SNAs can be induced by small noise in autonomous discrete-time maps and in periodically driven continuous-time systems. These attractors, which are relevant to physical and biological applications, can thus be expected to occur more commonly in dynamical systems than previously thought.

Logistic Models↗

PubMed2004

Error function attack of chaos synchronization based encryption schemes.

Different chaos synchronization based encryption schemes are reviewed and compared from the practical point of view. As an efficient cryptanalysis tool for chaos encryption, a proposal based on the error function attack is presented systematically and used to evaluate system security. We define a quantitative measure (quality factor) of the effective applicability of a chaos encryption scheme, which takes into account the security, the encryption speed, and the robustness against channel noise. A comparison is made of several encryption schemes and it is found that a scheme based on one-way coupled chaotic map lattices performs outstandingly well, as judged from quality factor.

Algorithms↗

PubMed2003

Complete synchronization and generalized synchronization of one-way coupled time-delay systems.

The complete synchronization and generalized synchronization (GS) of one-way coupled time-delay systems are studied. We find that GS can be achieved by a single scalar signal, and its synchronization threshold for different delay times shows the parameter resonance effect, i.e., we can obtain stable synchronization at a smaller coupling if the delay time of the driven system is chosen such that it is in resonance with the driving system. Near chaos synchronization, the desynchronization dynamics displays periodic bursts with the period equal to the delay time of the driven system. These features can be easily applied to the recovery of time-delay systems.

Journal Article↗

PubMed2003

Measure synchronization in coupled phi4 Hamiltonian systems.

Transitions to measure synchronization both in the quasiperiodic and chaotic cases are investigated based on numerical computation of two coupled phi(4) equations. Some relevant quantities such as the bare energies, the interaction energy, and the phase difference of the two oscillators are computed to clarify the characteristics of the transitions and the measure-synchronous states. A bifurcation with discontinuous bare energy and continuous interaction energy, which takes the maximum value at the critical point, is found for the transition from the desynchronous quasiperiodic state to the measure-synchronous quasiperiodic state, and the related power law scalings are deduced. Stick-slip and random-walk-like behavior of the phase difference is found for the chaotic measure-synchronous state, and this explains the monotonous increase of the interaction energy with an increase of coupling.

Journal Article↗

PubMed2002

Transitions from partial to complete generalized synchronizations in bidirectionally coupled chaotic oscillators.

Generalized synchronization in an array of mutually (bidirectionally) coupled nonidentical chaotic oscillators is studied. Coupled Lorenz oscillators and coupled Lorenz-Rossler oscillators are adopted as our working models. With increasing the coupling strengths, the system experiences a cascade of transitions from the partial to the global generalized synchronizations, i.e., different oscillators are gradually entrained through a clustering process. This scenario of transitions reveals an intrinsic self-organized order in groups of interacting units, which generalizes the idea of generalized synchronizations in drive-response systems.

Journal Article↗