Chinese Physics B

Xia, Li-Li; Chen, Li-Qun; Fu, Jing-Li; Wu, Jing-He

doi: 10.1088/1674-1056/23/7/070201pmid: N/A

We present a numerical simulation method of Noether and Lie symmetries for discrete Hamiltonian systems. The Noether and Lie symmetries for the systems are proposed by investigating the invariance properties of discrete Lagrangian in phase space. The numerical calculations of a two-degree-of-freedom nonlinear harmonic oscillator show that the difference discrete variational method preserves the exactness and the invariant quantity.

Nong, Li-Juan; Zhang, Da-Juan

doi: 10.1088/1674-1056/23/7/070202pmid: N/A

A non-autonomous 3-component discrete Boussinesq equation is discussed. Its spacing parameters pn and qm are related to independent variables n and m, respectively. We derive bilinear form and solutions in Casoratian form. The plain wave factor is defined through the cubic roots of unity. The plain wave factor also leads to extended non-autonomous discrete Boussinesq equation which contains a parameter . Tree-dimendional consistency and Lax pair of the obtained equation are discussed.

Wang, Xin; Chen, Yong

doi: 10.1088/1674-1056/23/7/070203pmid: N/A

Novel explicit rogue wave solutions of the coupled Hirota equations are obtained by using the Darboux transformation. In contrast to the fundamental Peregrine solitons and dark rogue waves, we present an interesting rogue-wave pair that involves four zero-amplitude holes for the coupled Hirota equations. It is significant that the corresponding expressions of the rogue-wave pair solutions contain polynomials of the fourth order rather than the second order. Moreover, dark-bright-rogue wave solutions of the coupled Hirota equations are given, and interactions between Peregrine solitons and dark-bright solitons are analyzed. The results further reveal the dynamical properties of rogue waves for the coupled Hirota equations.

Mu, Wen-Ying; Cui, Bao-Tong; Lou, Xu-Yang; Li, Wen

doi: 10.1088/1674-1056/23/7/070204pmid: N/A

This paper aims to improve the performance of a class of distributed parameter systems for the optimal switching of actuators and controllers based on event-driven control. It is assumed that in the available multiple actuators, only one actuator can receive the control signal and be activated over an unfixed time interval, and the other actuators keep dormant. After incorporating a state observer into the event generator, the event-driven control loop and the minimum inter-event time are ultimately bounded. Based on the event-driven state feedback control, the time intervals of unfixed length can be obtained. The optimal switching policy is based on finite horizon linear quadratic optimal control at the beginning of each time subinterval. A simulation example demonstrate the effectiveness of the proposed policy.

Lakshmanan, S.; Park, Ju H.; Rihan, Fathalla A.; Rakkiyappan, R.

doi: 10.1088/1674-1056/23/7/070205pmid: N/A

We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate LyapunovKrasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.

Guo, Jin-Li

doi: 10.1088/1674-1056/23/7/070206pmid: N/A

The principle that ‘the brand effect is attractive’ underlies the preferential attachment. Here we show that the brand effect is just one dimension of attractiveness. Another dimension is competitiveness. We firstly introduce a general framework that allows us to investigate the competitive aspect of real networks, instead of simply preferring popular nodes. Our model accurately describes the evolution of social and technological networks. The phenomenon that more competitive nodes become richer can help us to understand the evolution of many competitive systems in nature and society. In general, the paper provides an explicit analytical expression of degree distributions of the network. In particular, the model yields a nontrivial time evolution of nodes' properties and the scale-free behavior with exponents depending on the microscopic parameters characterizing the competition rules. Secondly, through theoretical analyses and numerical simulations, we reveal that our model has not only the universality for the homogeneous weighted network, but also the character for the heterogeneous weighted network. Thirdly, we also develop a model based on the profit-driven mechanism. It can better describe the observed phenomenon in enterprise cooperation networks. We show that the standard preferential attachment, the growing random graph, the initial attractiveness model, the fitness model, and weighted networks can all be seen as degenerate cases of our model.

Qin, Yi-Xiao; Liu, Ying-Ying; Li, Zhong-Hua; Yang, Ming

doi: 10.1088/1674-1056/23/7/070207pmid: N/A

An interpolating reproducing kernel particle method for two-dimensional (2D) scatter points is introduced. It eliminates the dependency of gridding in numerical calculations. The interpolating shape function in the interpolating reproducing kernel particle method satisfies the property of the Kronecker delta function. This method offers a mathematics basis for recognition technology and simulation analysis, which can be expressed as simultaneous differential equations in science or project problems. Mathematical examples are given to show the validity of the interpolating reproducing kernel particle method.

Zhang, Hong; Song, Song-He; Chen, Xu-Dong; Zhou, Wei-En

doi: 10.1088/1674-1056/23/7/070208pmid: N/A

The energy preserving average vector field (AVF) method is applied to the coupled SchrödingerKdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants.

Xu, Xue-Xiang; Yuan, Hong-Chun; Wang, Yan

doi: 10.1088/1674-1056/23/7/070301pmid: N/A

We investigate the nonclassical properties of arbitrary number photon annihilation-then-creation operation (AC) and creation-then-annihilation operation (CA) to the thermal state (TS), whose normalization factors are related to the polylogarithm function. Then we compare their quantum characters, such as photon number distribution, average photon number, Mandel Q-parameter, purity and the Wigner function. Because of the noncommutativity between the annihilation operator and the creation operator, the ACTS and the CATS have different nonclassical properties. It is found that nonclassical properties are exhibited more strongly after AC than after CA. In addition we also examine their non-Gaussianity. The result shows that the ACTS can present a slightly bigger non-Gaussianity than the CATS.

Li, Ji-Qiang; Zhou, Bin

doi: 10.1088/1674-1056/23/7/070302pmid: N/A

We investigate global entanglement in the ground state of single-molecular magnet Na9[Cu3Na3(H2O)9(-AsW9O33)2]·26H2O with an external magnetic field. The concurrence, tangle, and measure function Q, which characterize the pairwise entanglement, 3-party entanglement and total entanglement, respectively, are calculated numerically at zero temperature. The results show that the magnitude and direction of the applied magnetic field play a significant role in the properties of three kinds of entanglement measures. We give a physical interpretation of the variation of the global entanglement with the magnetic field. Finally, the phase diagram of the global entanglement characterized by the critical magnetic fields is presented.