Chinese Physics B

Zhang, Zhen-Gang; Ding, Zhuo; Fan, Jing-Fang; Meng, Jun; Ding, Yi-Min; Ye, Fang-Fu; Chen, Xiao-Song

doi: 10.1088/1674-1056/24/9/090201pmid: N/A

The concept of smart city gives an excellent resolution to construct and develop modern cities, and also demands infrastructure construction. How to build a safe, stable, and highly efficient public transportation system becomes an important topic in the process of city construction. In this work, we study the structural and robustness properties of transportation networks and their sub-networks. We introduce a complementary network model to study the relevance and complementarity between bus network and subway network. Our numerical results show that the mutual supplement of networks can improve the network robustness. This conclusion provides a theoretical basis for the construction of public traffic networks, and it also supports reasonable operation of managing smart cities.

Syed Ali, M.; Saravanakumar, R.

doi: 10.1088/1674-1056/24/9/090202pmid: N/A

This paper is concerned with the problem of delay-dependent robust H∞ control for a class of uncertain systems with two additive time-varying delays. A new suitable Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and a tighter upper bound of the derivative of the LKF is derived. By applying a convex optimization technique, new delay-dependent robust H∞ stability criteria are derived in terms of linear matrix inequalities (LMI). Based on the stability criteria, a state feedback controller is designed such that the closed-loop system is asymptotically stable. Finally, numerical examples are given to illustrate the effectiveness of the proposed method. Comparison results show that our results are less conservative than the existing methods.

Hu, Xiao-Rui; Chen, Yong

doi: 10.1088/1674-1056/24/9/090203pmid: N/A

For the (2+1)-dimensional Broer–Kaup–Kupershmidt (BKK) system, the nonlocal symmetries related to the Schwarzian variable and the corresponding transformation group are found. Moreover, the integrability of the BKK system in the sense of having a consistent Riccati expansion (CRE) is investigated. The interaction solutions between soliton and cnoidal periodic wave are explicitly studied.

Dong, Hao; Nie, Yu-Feng; Cui, Jun-Zhi; Wu, Ya-Tao

doi: 10.1088/1674-1056/24/9/090204pmid: N/A

We study the hyperbolic–parabolic equations with rapidly oscillating coefficients. The formal second-order two-scale asymptotic expansion solutions are constructed by the multiscale asymptotic analysis. In addition, we theoretically explain the importance of the second-order two-scale solution by the error analysis in the pointwise sense. The associated explicit convergence rates are also obtained. Then a second-order two-scale numerical method based on the Newmark scheme is presented to solve the equations. Finally, some numerical examples are used to verify the effectiveness and efficiency of the multiscale numerical algorithm we proposed.

Chen, Yao-Deng; Yang, Hong-Wei; Gao, Yu-Fang; Yin, Bao-Shu; Feng, Xing-Ru

doi: 10.1088/1674-1056/24/9/090205pmid: N/A

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space. Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves, the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves, the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

Bai, Lu; Chen, Fei; Lan, Wei-Yao

doi: 10.1088/1674-1056/24/9/090206pmid: N/A

This paper considers the formation tracking problem under a rigidity framework, where the target formation is specified as a minimally and infinitesimally rigid formation and the desired velocity of the group is available to only a subset of the agents. The following two cases are considered: the desired velocity is constant, and the desired velocity is time-varying. In the first case, a distributed linear estimator is constructed for each agent to estimate the desired velocity. The velocity estimation and a formation acquisition term are employed to design the control inputs for the agents, where the rigidity matrix plays a central role. In the second case, a distributed non-smooth estimator is constructed to estimate the time-varying velocity, which is shown to converge in a finite time. Theoretical analysis shows that the formation tracking problem can be solved under the proposed control algorithms and estimators. Simulation results are also provided to show the validity of the derived results.

Liu, Xian; Miao, Dong-Kai; Gao, Qing; Xu, Shi-Yun

doi: 10.1088/1674-1056/24/9/090207pmid: N/A

Neural mass models can simulate the generation of electroencephalography (EEG) signals with different rhythms, and therefore the observation of the states of these models plays a significant role in brain research. The structure of neural mass models is special in that they can be expressed as Lurie systems. The developed techniques in Lurie system theory are applicable to these models. We here provide a new observer design method for neural mass models by transforming these models and the corresponding error systems into nonlinear systems with Lurie form. The purpose is to establish appropriate conditions which ensure the convergence of the estimation error. The effectiveness of the proposed method is illustrated by numerical simulations.

Liu, Wei; Liu, Ai-Li; Zhou, Shao-Lei

doi: 10.1088/1674-1056/24/9/090208pmid: N/A

This paper studies the distributed H∞ control problem of identical linear time invariant multi-agent systems subject to external disturbances. A directed graph containing a spanning tree is used to model the communication topology. Based on the relative states of the neighbor agents and a subset of absolute states of the agents, distributed static H∞ controllers are proposed. The concept of an H∞ performance region is extended to the directed graph situation. Then the results are used to solve the leader–follower H∞ consensus problem. Sufficient conditions are proposed based on bounded real lemma and algebraic graph theory. The effectiveness of the theoretical results is illustrated via numerical simulations.

Ma, Ya-Yan; Wang, Bao-Yun

doi: 10.1088/1674-1056/24/9/090209pmid: N/A

Security against eavesdroppers is a critical issue in cognitive radio networks (CRNs). In this paper, a scenario consisting of one primary pair and multiple secondary pairs is considered. The secondary transmitters (STs) work in half-duplex mode and they are potential eavesdroppers on the primary transmission unless they are allowed to simultaneously transmit with the primary transmitter (PT). A modified second-price sealed-bid auction scheme is employed to model the interaction between the PT and STs. With the proposed auction scheme, the hostile relationship between the PT and STs is transformed into a cooperative relationship. An iterative algorithm based on the max–min criteria is proposed to find the optimal bidding power of the STs for an access chance in the presence of multiple eavesdroppers. Numerical results show that the proposed auction scheme not only improves the PT’s security but also increases the access opportunities of the STs.

Ma, Yu-Quan

doi: 10.1088/1674-1056/24/9/090301pmid: N/A

We investigate the ground-state Riemannian metric and the cyclic quantum distance of an inhomogeneous quantum spin-1/2 chain in a transverse field. This model can be diagonalized by using a general canonical transformation to the fermionic Hamiltonian mapped from the spin system. The ground-state Riemannian metric is derived exactly on a parameter manifold ring S1, which is introduced by performing a gauge transformation to the spin Hamiltonian through a twist operator. The cyclic ground-state quantum distance and the second derivative of the ground-state energy are studied in different exchange coupling parameter regions. Particularly, we show that, in the case of exchange coupling parameter Ja = Jb, the quantum ferromagnetic phase can be characterized by an invariant quantum distance and this distance will decay to zero rapidly in the paramagnetic phase.