Chen Shi-Gang

Scaling Property of Period-n-Tupling Sequences in One-Dimensional Mappings

We calculated the universal scaling function and the scaling factor as well as the convergence rate for periodtripling, -quadrapling and–quintupling sequences of and types. The superstable periods are closely connected to a set of polynomial defined recursively by the original mapping. Some notable properties of these polynomials are studied. Several approaches to solving the renormalization group equation and estimating the scaling factors are suggested.

Elimination of Spiral Waves and Competition between Travelling Wave Impulses and Spiral Waves

The interaction between travelling wave impulses and spiral waves is studied and the results of their competition are related to the exciting period. From the results, it is known that the formation and development of spiral waves in cardiac tissue depend on the period by which the travelling wave impulses are excited. A method is proposed to eliminate spiral waves, which is easily operated.

Synchronization and Asynchronization in Two Coupled Excitable Systems

The synchronization and asynchronization of two coupled excitable systems are investigated. The two systems with different initial configurations, which are separately a single spiral wave (or a travel wave) and the rest state, can be developed to the synchronizing state with the same spiral wave (or travel wave) in each system, when the coupling is very strong. Decreasing the coupling intensity, two rest states or two different configurations appear in the two systems. The qualitative analysis and interpretation are given.

Control of Spiral Waves and Spatiotemporal Chaos by Exciting Travel Wave Trains

Spiral waves and spatiotemporal chaos usually are harmful and need to be suppressed. In this paper, a method is proposed to control them. Travel wave trains can be generated by periodic excitations near left boundary, spiral waves and spatiotemporal chaos can be eliminated by the trains for some certain excitation periods. Obvious resonant behavior can be observed from the relation between the periods of the trains and excitation ones. The method is against noise.

Symmetriy Analysis of Convection Patterns

In this paper, we carry out a symmetry analysis of convection patterns of Newton-Boussinesq fluid in some finite containers. We also discuss, from the viewpoint of symmetry analysis, the behaviour of infinitely extended fluid layer, as a limit of that in finite container, near convection threshold.

Effect of Asymmetric Potential and Gaussian Colored Noise on Stochastic Resonance

The phenomenon of stochastic resonance (SR) in a bistable nonlinear system is studied when the system is driven by the asymmetric potential and additive Gaussian colored noise. Using the unified colored noise approximation method, the additive Gaussian colored noise can be simplified to additive Gaussian white noise. The signal-to-noise ratio (SNR) is calculated according to the generalized two-state theory (shown in [H.S. Wio and S. Bouzat, Brazilian J. Phys. 29 (1999) 136]). We find that the SNR increases with the proximity of a to zero. In addition, the correlation time τ between the additive Gaussian colored noise is also an ingredient to improve SR. The shorter the correlation time τ between the Gaussian additive colored noise is, the higher of the peak value of SNR.

Elimination of spiral waves and spatiotemporal chaos by the pulse with a specific spatiotemporal configuration

Spiral waves and spatiotemporal chaos are sometimes harmful and should be controlled. In this paper spiral waves and spatiotemporal chaos are successfully eliminated by the pulse with a very specific spatiotemporal configuration. The excited position D of spiral waves or spatiotemporal chaos is first recorded at an arbitrary time (t0). When the system at the domain D enters a recovering state, the external pulse is injected into the domain. If the intensity and the working time of the pulse are appropriate, spiral waves and spatiotemporal chaos can finally be eliminated because counter-directional waves can be generated by the pulse. There are two advantages in the method. One is that the tip can be quickly eliminated together with the body of spiral wave, and the other is that the injected pulse may be weak and the duration can be very short so that the original system is nearly not affected, which is important for practical applications.

Ionization Dynamics of 1D Model Atom in Ultra-Strong 1ω-2ω Laser Fields*

We investigate the ionization dynamics of 1D model atom in ultra-strong dichromatic 1ω-2ω laser fields with a constant phase difference. We find numerically that both the total ionization and the distribution between forward and backward rates show clear phasedependent character. This phenomenon can be explained by the first-order high frequency Floquet theory. Finally, this phase-dependent character is testified with pulsed laser fields provided the pulse is smoothly (adiabatically) turned on.

Localization in the Non-analytic Quantum Kicked Systems*

Numerical investigations on non-analytic quantum kicked systems are presented. A new type of localization - power-law localization is found to be universal in the nonanalytic systems. With increasing the perturbation strength, a transition from perturbative localization to pseudo-integrable system, to dynamical localization and to complete extension is clearly demonstrated. The dependence of the localization length on perturbation is given in different parameter regimes.Numerical investigations on non-analytic quantum kicked systems are presented. A new type of localization — power-law localization is found to be universal in the non-analytic systems. With increasing the perturbation strength, a transition from perturbative localization to pseudo-integrable system, to dynamical localization and to complete extension is clearly demonstrated. The dependence of the localization length on perturbation is given in different parameter regimes.

Finding and Control of Unstable Periodic Orbit in Autonomous Differential System

A new method used to control unstable periodic orbit is presented. This method can reduce the three-dimensional system into two-dimensional by considering an appropriate variable equation as free equation. It is also effective in the presence of noise.