Search

This paper features a survey of some recent developments in asymptotic techniques, which are valid not only for weakly nonlinear equations, but also for strongly ones. Further, the obtained approximate analytical solutions are valid for the whole solution domain. The limitations of traditional perturbation methods are illustrated, various modified perturbation techniques are proposed, and some mathematical tools such as variational theory, homotopy technology, and iteration technique are introduced to overcome the shortcomings. In this paper the following categories of asymptotic methods are emphasized: (1) variational approaches, (2) parameter-expanding methods, (3) parameterized perturbation method, (4) homotopy perturbation method (5) iteration perturbation method, and ancient Chinese methods. The emphasis of this article is put mainly on the developments in this field in China so the references, therefore, are not exhaustive. [ABSTRACT FROM AUTHOR]

In this paper, a nonlinear state observer control strategy is developed for projective self-synchronization of the fractional-order chaotic attractors of a permanent magnet synchronous motor (PMSM) system. The mathematical model of PMSM system in a smooth fractional-order form is derived by using the fractional derivative theory. A state observer control design can achieve the full-state projective synchronization of the fractional-order PMSM (FO-PMSM) system without the limitation of partial-linearity. Global stability and asymptotic synchronization between the outputs of drive system and response system can be obtained. Simulation results are provided to demonstrate the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

This paper studies full state hybrid projective synchronization of the unified chaotic system with unknown parameters. Based on the Lyapunov stability theory, an adaptive controller is designed. It is proved theoretically that the controller can make the states of the dynamical system and the response system with unknown parameters asymptotically full state hybrid projective synchronized. Numerical simulations show the effectiveness of the scheme. [ABSTRACT FROM AUTHOR]

Bipartite network with rewiring dynamics exists in many real-world networks. Various models based on the mean-field approximation are successfully proposed for the degree distribution of rewiring dynamics in the bipartite network. However, there are implicit or even obvious differences among these models, despite that they are utilized for modeling the same rewiring problem. How the differences among these models arise and how the differences influence the solution of the degree distribution remain unresolved. Firstly, the models for a bipartite network with rewiring dynamics are categorized into three versions, which are named as a two steps version model (TSV model), a one step version-I model (OSV-I model), and a one step version-II model (OSV-II model) in the present paper. The differences among the three versions models are clarified. Then, we derive an exact solution for the TSV model and that for the OSV-II model. Furthermore, we prove that the exact solution for the steady degree distribution of the TSV model and that of the OSV-II model are globally asymptotically stable. Based on the exact solutions, the differences of the solution of the degree distribution among the three versions models are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of heat exchange in a composite plane wall whose heat transmitting coefficient is a stationary random field. We present a method of multiscale asymptotic expansions and the corresponding finite element method to solve the problem. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of heat exchange in composite plane wall whose heat transmitting coefficient is not a locally periodic function. For that problem, we present a method of multiscale asymptotic expansions and then propose its corresponding FE algorithm. Of course, we give comprehensive theoretical analysis for the FE algorithm. Finally, we use numerical experiments to investigate them. [ABSTRACT FROM AUTHOR]

This paper designs the controller for uncertain Lorenz system with multiple inputs containing sector nonlinearities and dead zone, and theoretically demonstrates the effectiveness of this controller. By this controller, the controlled Lorenz system can asymptotically drive the system orbits to arbitrarily objective trajectories even with uncertainties and sector nonlinearities and dead zone in the inputs, and thus has strong robustness. Finally, through the emulation studies of controlled Lorenz systems, it demonstrates the effectiveness of this controller. [ABSTRACT FROM AUTHOR]

This paper is concerned with modified integration algorithm in the strain space for rate and temperature dependent elasto-plastic constitutive relations in order to obtain more accurate results in numerical implementation. The proposed algorithm adopts both the 2-stage Lobatto IIIA with second-order accuracy and the iteration procedure using the Newton–Raphson method to enfoce consistency at the end of the step. The algorithm enables to consider the convective stress rates on the yield surface in the strain space in the numerical integration of the constitutive model. Accuracy assessment using the isoerror maps and FEM analysis of the adiabatic shear band is carried out in order to demonstrate the accuracy of the proposed algorithm. [ABSTRACT FROM AUTHOR]