Stochastic period-doubling bifurcation analysis of a Rssler system with a bounded random parameter

This paper aims to study the stochastic period-doubling bifurcation of the three-dimensional Rssler system with an arch-like bounded random parameter. First, we transform the stochastic Rssler system into its equivalent deterministic one in the sense of minimal residual error by the Chebyshev polynomial approximation method. Then, we explore the dynamical behaviour of the stochastic Rssler system through its equivalent deterministic system by numerical simulations. The numerical results show that some stochastic period-doubling bifurcation, akin to the conventional one in the deterministic case, may also appear in the stochastic Rssler system. In addition, we also examine the influence of the random parameter intensity on bifurcation phenomena in the stochastic Rssler system.     

Theoretical Study on Drift of Ca^2＋ Spiral Waves Controlled by Electric Field

Based on the Tang-Othmer Ca^2＋ model, the drift behavior of intracellular Ca^2＋ spiral waves under the influence of weak electric field is investigated. Numerical results show that the dependence of drift velocity of the spiral tip on dc electric field is similar to experimental observations in BZ system. When an ac electric field is applied, interesting resonant-drift phenomenon is observed with ω=2ω0. All results can be explained analytically using a proximate method.     

Multi-mode Spiral Wave in a Coupled Oscillatory Medium

Multi-mode spiral wave and its breakup in 1-d and 2-d coupled oscillatory media is studied here by theoretic analysis and numerical simulations. The analysis in 1-d system shows that the dispersion relation curve could be nonmonotonic depending on the coupling strength. It may also lead to the coexistence of different wave numbers within one system. Direct numerical observations in 1-d and 2-d systems conform to the prediction of dispersion relation analysis. Our findings indicate that the wave grouping can also be observed in oscillatory media without tip meandering and waves with negative group velocity can occur without inhomogeneity.     

Suppression of Spiral Wave in Modified Orengonator Model

In this paper, a spatial perturbation scheme is proposed to suppress the spiral wave in the modified Orengonator model, which is used to describe the chemical reaction in the light-sensitive media. The controllable external illumination Ф is perturbed with a spatial linear function. In our numerical simulation, the scheme is investigated by imposing the external controllable illumination on the space continuously and/or intermittently. The numerical simulation results confirm that the stable rotating spiral wave still can be removed with the scheme proposed in this paper even if the controllable Ф changed vs. time and space synchronously. Then the scheme is also used to control the spiral wave and turbulence in the modified Fitzhugh-Nagumo model. It is found that the scheme is effective to remove the sable rotating and meandering spiral wave but it costs long transient period and intensity of the gradient parameter to eliminate the soiral turbulence.     

Spiral Wave in Small-World Networks of Hodgkin-Huxley Neurons

The effect of small-world connection and noise on of Hodgkin-Huxley neurons are investigated in detail. Some the formation and transition of spiral wave in the networks interesting results are found in our numerical studies, i） The quiescent neurons are activated to propagate electric signal to others by generating and developing spiral wave from spiral seed in small area. ii） A statistical factor is defined to describe the collective properties and phase transition induced by the topology of networks and noise, iii） Stable rotating spiral wave can be generated and keeps robust when the rewiring probability is below certain threshold, otherwise, spiral wave can not be developed from the spiral seed and spiral wave breakup occurs for a stable rotating spiral wave. iv） Gaussian white noise is introduced on the membrane of neurons to study the noise-induced phase transition on spiral wave in small-world networks of neurons. It is confirmed that Ganssian white noise plays active role in supporting and developing spiral wave in the networks of neurons, and appearance of smaller factor of synchronization indicates high possibility to induce spiral wave.     

Energy band structure in optical of spin-1 condensates lattices

The energy band structure of spin-1 condensates with repulsive spimindependent and either ferromagnetic or antiferromagnetic spin-dependent interactions in one-dimensional （1D） periodic optical lattices is discussed. Within the two-mode approximation, Bloch bands of spin-1 condensates are presented. The results show that the Bloch bands exhibit a complex structure as the atom density of mF = 0 hyperfine state increases： bands splitting, reversion, intersection and loop structure are excited subsequently. The complex band structure should be related to the tunneling and spin-mixing dynamics.     

Control of Spiral Waves in an Excitable Medium by Applying Close Loop Feedback Scheme

In this paper, a scheme of close-loop feedback is proposed to induce transition of spiral pattern in the excitable media, which is described with the modified FitzHugh-Nagumo model. The numerical simulation results confirm that the stable rotating spiral wave is removed and the whole media becomes homogeneous when appropriate intensity of feedback is used no matter whether the coupling feedback is imposed on the whole media or the sites in one line in the media.     

Dynamics of Spiral Wave Tip in Excitable Media with Gradient Parameter

Using a Barkley model as an example, we study spirM waves and spiral tips in a gradient excitable medium. The gradient distribution of parameters is introduced to depict the inhomogeneous medium. It is found that the parameter fluctuations play an important role in the morphology of spiral pattern and the movements of spiral tips. For varied gradient parameters, it is observed that there exist three kinds of spiral behaviors, stable rotation, rebound of spiral tip from the boundary, and spiral breakup.     

Enhanced Synchronization of Intercellular Calcium Oscillations by Noise Contaminated Signals

We consider the dynamics of locally coupled calcium oscillation systems, each cell is subjected to extracellular contaminated signal, which contains common sub-threshold signal and independent Gaussian noise. It is found that intermediate noise can enhance synchronized oscillations of calcium ions, where the frequency of noise-induced oscillations is matched with the one of sub-threshold external signal. We show that synchronization is enhanced as a result of the entrainment of external signal. Furthermore, the effect of coupling strength is considered. We find above-mentioned phenomenon exists only when coupling strength is very small. Our findings may exhibit that noise can enhance the detection of feeble external signal through the mechanism of synchronization of intercellular calcium ions.     

Electronic dynamic behavior in inductively coupled plasmas with radio-frequency bias

The inflexion point of electron density and effective electron temperature curves versus radio-frequency （RF） bias voltage is observed in the H mode of inductively coupled plasmas （ICPs）. The electron energy probability function （EEPF） evolves first from a Maxwellian to a Druyvesteyn-like distribution, and then to a Maxwellian distribution again as the RF bias voltage increases. This can be explained by the interaction of two distinct bias-induced mechanisms, that is： bias- induced electron heating and bias-induced ion acceleration loss and the decrease of the effective discharge volume due to the sheath expansion. Furthermore, the trend of electron density is verified by a fluid model combined with a sheath module.     

Quantum Information Processing in a Coupled Cavity Array

We consider a one-dimensional array of L identical coupled cavities, and each cavity is doped with a two-level qubit. Experimentally, it has been developed in several varieties by the newest technology. We find that the one-qubit quantum state can be perfectly transferred through the cavity array, and the entanglement between the first two qubits can also be transferred to the last two qubits. In addition, we successfully realized the entangling gate and swap gate in the coupled cavity array.     

Characteristics of dual-frequency capacitively coupled SF_6/O_2 plasma and plasma texturing of multi-crystalline silicon

Due to it being environmentally friendly, much attention has been paid to the dry plasma texturing technique serving as an alternative candidate for multicrystalline silicon(mc-Si) surface texturing. In this paper, capacitively coupled plasma(CCP) driven by a dual frequency(DF) of 40.68 MHz and 13.56 MHz is first used for plasma texturing of mc-Si with SF6/O2gas mixture. Using a hairpin resonant probe and optical emission techniques, DF-CCP characteristics and their influence on mc-silicon surface plasma texturing are investigated at different flow rate ratios, pressures, and radio-frequency(RF)input powers. Experimental results show that suitable plasma texturing of mc-silicon occurs only in a narrow range of plasma parameters, where electron density n9e must be larger than 6.3 × 10cm-3and the spectral intensity ratio of the F atom to that of the O atom([F]/[O]) in the plasma must be between 0.8 and 0.3. Out of this range, no cone-like structure is formed on the mc-silicon surface. In our experiments, the lowest reflectance of about 7.3% for mc-silicon surface texturing is obtained at an [F]/[O] of 0.5 and ne of 6.9 × 109cm-3.     

Entanglement of two two-level atoms trapped in coupled cavities with a Kerr medium

In this paper, the entanglement dynamics of two two-level atoms trapped in coupled cavities with a Kerr medium is investigated, We find that the phenomena of entanglement sudden death （ESD） and entanglement sudden birth （ESB） appear during the evolution process. The influences of initial atomic states, Kerr medium, and cavity-cavity hopping rate on the atom-atom entanglement are discussed. The results obtained by the numerical method show that the atom- atom entanglement is strengthened and even prevented from ESD with increasing cavity-cavity hopping rate and Kerr nonlinearity.     

A Simple Framework of Conservative Algorithms for the Coupled Nonlinear Schrodinger Equations with Multiply Components

Considering the coupled nonlinear Schrodinger system with multiply components, we provide a novel framework for constructing energy-preserving algorithms. In detail, based on the high order compact finite difference method, Fourier pseudospectral method and wavelet collocation method for spatial discretizations, a series of high accurate conservative algorithms are presented. The proposed algorithms can preserve the corresponding discrete charge and energy conservation laws exactly, which would guarantee their numerical stabilities during long time computations. Furthermore, several analogous multi-symplectic algorithms are constructed as comparison. Numerical experiments for the unstable plane waves will show the advantages of the proposed algorithms over long time and verify the theoretical analysis.     

Darboux Transformation and Soliton Solutions for Inhomogeneous Coupled Nonlinear Schrodinger Equations with Symbolic Computation

With the aid of computation, we consider the variable-coefficient coupled nonlinear Schrodinger equations with the effects of group-velocity dispersion, self-phase modulation and cross-phase modulation, which have potential applications in the long-distance communication of two-pulse propagation in inhomogeneous optical fibers. Based on the obtained nonisospectral linear eigenvalue problems （i.e. Lax pair）, we construct the Darboux transformation for such a model to derive the optical soliton solutions. In addition, through the one- and two-soliton-like solutions, we graphically discuss the features of picosecond solitons in inhomogeneous optical fibers.     

Painleve Property and Complexiton Solutions of a Special Coupled KdV Equation

A special coupled KdV equation is proved to be the Painleve property by the Kruskal＇s simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota＇s bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically.     

Three-dimensional solitons in two-component Bose-Einstein condensates

We investigate a kind of solitons in the two-component Bose-Einstein condensates with axisymmetric configurations in the R2 × S1 space. The corresponding topological structure is referred to as Hopfion. The spin texture differs from the conventional three-dimensional （3D） skyrmion and knot, which is characterized by two homotopy invariants. The stability of the Hopfion is verified numerically by evolving the Gross-Pitaevskii equations in imaginary time.     

A New Type of Seiberg-Witten Map and Its Application

Deformation quantization is a powerful tool to deal with systems in noncommutative space to get their energy spectra and corresponding Wigner functions, especially for the ease of both coordinates and momenta being noneommutative. In order to simplify solutions of the relevant .-genvalue equation, we introduce a new kind of Seiberg Witten-like map to change the variables of the noncommutative phase space into ones of a commutative phase space, and demonstrate its role via an example of two-dimensional oscillator with both kinetic and elastic couplings in the noneommutative phase space.     

Considering Backward Effect in Coupled Map Car-Following Model

Based on the pioneer work of Konishi et al., a new control method is proposed to suppress the traffic congestion in the coupled map （CM） car-following model under open boundary condition. The influence of the following car to the system has been considered. Our method and that presented by Konishi et al. [Phys. Rev. E 60 （1999） 4000] are compared. Although both the methods could suppress the traffic jam, the simulation results show that the temporal behavior obtained by ours is better than that proposed by the Konishi＇s et al. The simulation results are consistent with the theoretical analysis.     

Soliton Solutions to Coupled Integrable Dispersionless Equations

In this paper, by introducing a new transformation, the bilinear form of the coupled integrable dispersionless （CID） equations is derived. It will be shown that this bilineax form is easier to perform the standard Hirota process. One-, two-, and three-soliton solutions are presented. Furthermore, the N-soliton solutions axe derived.