Stability of antiperiodic recurrent neural networks with multiproportional delays

In general, a proportional function is obviously not antiperiodic, yet a very interesting fact in this paper shows that it is possible there is an antiperiodic solution for some proportional delayed dynamical systems. We deal with the issue of antiperiodic solutions for RNNs (recurrent neural networks) incorporating multiproportional delays. Employing Lyapunov method, inequality techniques and concise mathematical analysis proof, sufficient criteria on the existence of antiperiodic solutions including its uniqueness and exponential stability are built up. The obtained results provide us some lights for designing a stable RNNs and complement some earlier publications. In addition, simulations show that the theoretical antiperiodic dynamics are in excellent agreement with the numerically observed behavior.     

Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks

In this paper, a new type of generalized Q-S (lag, anticipated, and complete) time-varying synchronization is defined. Adaptive Q-S (lag, anticipated, and complete) time-varying synchronization and parameters identification of uncertain delayed neural networks have been considered, where the delays are multiple time-varying delays. A novel control method is given by using the Lyapunov functional method. With this new and effective method, parameters identification and Q-S (lag, anticipated, and complete) time-varying synchronization can be achieved simultaneously. Simulation results are given to justify the theoretical analysis in this paper.     

An adaptive chaotic secure communication scheme with channel noises

In this Letter, an adaptive secure communication scheme with channel noises is proposed. Based on the idea of chaotic masking-modulation, the message is encrypted by a chaotic signal. By using adaptive feedback control techniques, the transmitter and the receiver are synchronized, so the masked signal can be perfectly recovered by the receiver in the presence of channel noises. In light of the Lyapunov stability theory for stochastic differential equations, several theoretical results are rigorously established. Finally, the famous Chua's circuits is used to illustrate the possible applications of the obtained theoretical results, and the computer simulations show that the proposed scheme is feasible and efficient.     

一类时滞种群模型的周期正解

利用一些分析技巧和重合度理论,研究了一类时滞种群模型：Ｎ’（ｔ）＝Ｎ（ｔ）「ｂ（ｔ）－∞／∑／ｊ＝１ａｊｌｎＮ（ｔ＝ｒｊ）」周期正解的存在性,得到了一些新的判据,同时也改进了一些相关文献的结果。     

Almost periodic solutions of n-species competitive system with feedback controls

In this paper, the following almost periodic n-species competitive system with feedback controls

     

Synchronization in an array of linearly stochastically coupled networks with time delays

In this paper, the complete synchronization problem is investigated in an array of linearly stochastically coupled identical networks with time delays. The stochastic coupling term, which can reflect a more realistic dynamical behavior of coupled systems in practice, is introduced to model a coupled system, and the influence from the stochastic noises on the array of coupled delayed neural networks is studied thoroughly. Based on a simple adaptive feedback control scheme and some stochastic analysis techniques, several sufficient conditions are developed to guarantee the synchronization in an array of linearly stochastically coupled neural networks with time delays. Finally, an illustrate example with numerical simulations is exploited to show the effectiveness of the theoretical results.     

一类高维时滞微分方程的周期解

本文考虑高维时滞微分方程ｘ′（ｔ）＝Ａ（ｔ,ｘ（ｔ））ｘ（ｔ）＋ｆ（ｔ,ｘ（ｔ－ｒ（ｔ）））其中（ｔ,ｘ）∈Ｒ^ｎ,Ａ（ｔ,ｘ）是ｎ×ｎ连续矩阵,ｆ（ｔ,ｘ）是ｎ维连续向量,ｒ（ｔ）是时间依赖的滞量,应用不动点定理,在确定的条件下,证明了该系统的周期解的存在性与唯一性     

Impulsive synchronization of coupled dynamical networks with nonidentical Duffing oscillators and coupling delays

This paper aims to investigate the synchronization problem of coupled dynamical networks with nonidentical Duffing-type oscillators without or with coupling delays. Different from cluster synchronization of nonidentical dynamical networks in the previous literature, this paper focuses on the problem of complete synchronization, which is more challenging than cluster synchronization. By applying an impulsive controller, some sufficient criteria are obtained for complete synchronization of the coupled dynamical networks of nonidentical oscillators. Furthermore, numerical simulations are given to verify the theoretical results.