A Note on ＂Global Exponential Convergence Analysis of Hopfield Neural Networks with Continuously Distributed Delays＂

In this note, we would like to point out that （i） of Corollary 1 given by Zhang et al. （cf Commun. Theor. Phys. 39 （2003） 381） is incorrect in general.     

Inverse chaos synchronization between bidirectionally coupled variable multiple time delay systems

We make first report on inverse chaos synchronization between bidirectionally non-linearly and linearly coupled variable multiple time delay laser systems governed by the Ikeda model. The results are of certain importance in secure chaos-based communication systems.     

Energy Decay for the Cauchy Problem of the Linear Wave Equation of Variable Coeffcients with Dissipation

Decay of the energy for the Cauchy problem of the wave equation of variable coeffcients with a dissipation is considered.It is shown that whether a dissipation can be localized near infinity depends on the curvature properties of a Riemannian metric given by the variable coeffcients.In particular,some criteria on curvature of the Riemannian manifold for a dissipation to be localized are given.     

求极限的等价无穷大代换

给出等价无穷大代换的法则,并由此得到求某些未定式极限的计算方法.     

具有HollingII类型功能反应的3种群捕食时滞模型

研究了具有HollingII类型功能反应的一捕食者有两个食饵的时滞系统,通过构造Lyapunov泛函得到了与时滞有关的系统全局渐近稳定的充分条件.     

Analysis on global exponential robust stability of reaction-diffusion neural networks with S-type distributed delays

To avoid the unstable phenomena caused by time delays and perturbations, we investigate the sufficient conditions to ensure the global exponential robust stability with a convergence rate for the reaction-diffusion neural networks with S-type distributed delays. Because S-type distributed delays lead to some difficulty, we also introduce a new generalized Halanay inequality and a novel method-system-approximation method into the qualitative research of neural networks. Moreover, the sufficient criteria provided here, which are rather accessible and feasible, have wider adaptive range.     

Asymptotic behaviour of the three-dimensional α-Navier-Stokes model with delays

We prove the existence and exponential stability of the stationary solutions for a three-dimensional α-Navier-Stokes model with delays. Instead of working directly with the model, we establish the results for a general abstract delay model, and then we apply them to our particular situation. We use two techniques in the stability analysis: the Lyapunov and Razumikhin approaches.     

Chaos synchronization and encoding in coupled semiconductor lasers of multiple modulated time delays

We numerically investigate the synchronization performance of unidirectionally and bidirectionally coupled chaotic semiconductor lasers subject to multiple modulated time delays optical feedbacks. Moreover, by studying the autocorrelation function of the coherent feedback semiconductor laser output, we find that the signatures of time delays can be erased in systems incorporating modulated feedback time delays, which largely improve the system security. Finally, chaos masking switching (CMS) is utilized to examine the communication ability. Numerical results indicate that the messages could be successfully recovered both in unidirectionally and bidirectionally coupled lasers, which confirms the possibility of applying multiple modulated delay system in optical chaos secure communication.