Adaptive robust convergence of neural networks with time-varying delays

This paper is concerned with the adaptive robust convergence for a class of neural networks with time-varying delays. By employing the Lyapunov method and a novel lemma, some delay-independent conditions are derived to guarantee the state variables of the discussed time-varying robust system to converge, globally, uniformly, exponentially to a ball in the state space with a pre-specified convergence rate. Here, the existence and uniqueness of the equilibrium point needs not to be considered. Finally, an illustrated example is given to show the effectiveness and usefulness of the results.     

Exponential synchronization of chaotic neural networks: a matrix measure approach

Based on matrix measure and Halanay inequality, exponential synchronization of a class of chaotic neural networks with time-varying delays is investigated. Without constructing Lyapunov function, some simple but generic criteria for exponential synchronization of chaotic neural networks are derived. It is shown that the obtained results are easy to verify and simple to implement in practice. Two examples are given to illustrate the effectiveness of the presented synchronization scheme.     

时间序列模型L_1-估计量的极限分布:平稳自回旧模型

时间序列模型的L_1-估计问题是非常重要的．这些估计量的许多性质都被研究过．然而，仍有一些基本问题有待解决．本文将给出平稳自回归模型L_1-估计量的极限分布．     

系数函数光滑度互不相同的变系数模型的一步估计法

该文提出了一种一步估计方法用以估计变系数模型中具有互不相同光滑度的未知函数, 所有未知函数和它们的导数的估计量由 一次极小化得到. 给出了估计量的渐近性质, 包括渐近偏差、方差和渐近分布, 一步估计量被证明达到了最优收敛速度.     

扩散系数小波估计的强相合性

本文研究了一维扩散方程中扩散系数的非参数估计,给出了有界Lipschitz扩散系数的线性小波估计,证明了所得估计量的强相合性.     

Time-delayed feedback control of dynamical small-world networks at Hopf bifurcation

We show that time-delayed feedback methods, which have successfully been used to control unstable steady states or periodic orbits, provide a tool to control Hopf bifurcation for a small-world network model with nonlinear interactions and time delays. We choose the interaction strength parameter as a bifurcation parameter. Without control, bifurcation will occur early; meanwhile, the model can maintain a stationary total influenced volume only in a certain domain of the interaction strength parameter. However, outside of this domain the model still possesses a stable total influenced volume that can be guaranteed by delayed feedback perturbation, and the onset of the Hopf bifurcation is postponed. The feedback perturbation vanishes if the stabilization is successful and thus the domain of stability can be extended under only small control force. We present an analytical investigation of the feedback scheme using characteristic equation and discuss effects of both a low-pass filter included in the control loop and nonzero latency times associated with generation and injection of the feedback signal.

     

Exponential stability in the mean square for stochastic neural networks with mixed time-delays and Markovian jumping parameters

In this paper, the stability analysis problem is considered for a class of stochastic neural networks with mixed time-delays and Markovian jumping parameters. The mixed delays include discrete and distributed time-delays, and the jumping parameters are generated from a continuous-time discrete-state homogeneous Markov process. The aim of this paper is to establish some criteria under which the delayed stochastic neural networks are exponentially stable in the mean square. By constructing suitable Lyapunov functionals, several stability conditions are derived on the basis of inequality techniques and the stochastic analysis. An example is also provided in the end of this paper to demonstrate the usefulness of the proposed criteria.     

Adaptive synchronization of uncertain dynamical networks with delayed coupling

We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains η _i will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, small-world, scale-free or random). Numerical examples with respectively nearest-neighbor coupling and scale-free structure are given to demonstrate the effectiveness of our presented scheme.     

Stability analysis and estimation of domain of attraction for the endemic equilibrium of an SEIQ epidemic model

This paper mainly addressed the stability analysis and the estimation of domain of attraction for the endemic equilibrium of a class of susceptible-exposed-infected-quarantine epidemic models. Firstly, we discuss the global stability of the disease-free equilibrium and the local stability of the endemic equilibrium in the feasible region D of the epidemic model, respectively. Secondly, we use a geometric approach to investigate the global stability of the endemic equilibrium in a positive invariant region \(D_s(\subset D)\). Furthermore, we estimates the domain of attraction for the endemic equilibrium via sum of squares optimization method, and obtain the optimal estimation by solving an semidefinite programming problem with sum of squares polynomial constraints. Finally, numerical simulation is examined to demonstrate the feasibility and effectiveness of the research results.     

Periodic bidirectional associative memory neural networks with distributed delays

Some sufficient conditions are obtained for the existence and global exponential stability of a periodic solution to the general bidirectional associative memory (BAM) neural networks with distributed delays by using the continuation theorem of Mawhin's coincidence degree theory and the Lyapunov functional method and the Young's inequality technique. These results are helpful for designing a globally exponentially stable and periodic oscillatory BAM neural network, and the conditions can be easily verified and be applied in practice. An example is also given to illustrate our results.