关于一类n维自映射扰动的稳定性

1981年,L.Block发现在一维自映射中,Sarkovskii定理对映射的扰动而言是稳定的.文[1]针对一类二维自映射,证明了其扰动也是稳定的,本文主要将这一扰动稳定性推广到可降的n维自映射中去.     

关于一类n维自映射的周期点集

设f是可降的n维自映射,给出了当f的周期点集是闭集时的一系列等价条件,将一维自映射的情形向更为一般的一类n维自映射推广.     

一类n维自映射有特殊异状点的充要条件

在一维自映射中，L．Block和Z．Nitecki分别指出了有特殊异状点、有异状点、有素周期点三者等价．本文主要给出有特殊异状点的一类n维自映射．     

一类n维自映射无异状点的充要条件

若f是可降的n维自映射,则可以利用可降映射的特征,给出了这类自映射无异状点的一个充要条件,当f限制在周期点集上时,是等度连续的。     

关于一类n维自映射扰动的稳定性

1981年,L.Block发现在一维自映射中,Sarkovskii定理对映射的扰动而言是稳定的。文[1]针对一类二维自映射,证明了其扰动也是稳定的,本文主要将这一扰动稳定性推广到可降的n维自映射中去。     

The analysis of complex behaviours of a novel three dimensional autonomous system

This paper introduces a new three dimensional autonomous system with five equilibrium points.It demonstrates complex chaotic behaviours within a wide range of parameters,which are described by phase portraits,Lyapunov exponents,frequency spectrum,etc.Analysis of the bifurcation and Poincar’e map is used to reveal mechanisms of generating these complicated phenomena.The corresponding electronic circuits are designed,exhibiting experimental chaotic attractors in accord with numerical simulations.Since frequency spectrum analysis shows a broad frequency bandwidth,this system has perspective of potential applications in such engineering fields as secure communication.     

Spectrum Analysis and Circuit Implementation of a New 3D Chaotic System with Novel Chaotic Attractors

The new autonomous system with only three equilibrium points is introduced. This system does not belong to the generalized Lorenz systems. The novel attractors are observed over a large range of parameters, which have rarely been reported in previous work. As an important component in chaotic signal generators, a physical circuit has been designed. The experimental results are in agreement with numerical simulations. More significantly, spectral analysis shows that the system has an extremely broad frequency spectral bandwidth in 0-131.6 Hz, without investigating any possible electronic techniques, which is more desirable for secure communications.     

Projective synchronisation with non-delayed and delayed coupling in complex networks consisting of identical nodes and different nodes

This paper first investigates the projective synchronisation problem with non-delayed and delayed coupling between drive-response dynamical networks consisting of identical nodes and different nodes.Based on Lyapunov stability theory,several nonlinear controllers are applied to achieve the projective synchronisation between the drive-response dynamical networks;simultaneously the topological structure of the drive dynamical complex networks can be exactly identified.Moreover,numerical examples are presented to verify the feasibility and effectiveness of the theorems.     

关于T2 3/4-分离型邻域空间

对邻域空间的研究已经有了一些结果,本文在此基础上引入了T_(2(3/4))-分离型邻域空间,着重讨论了它的重要性质,并给出两个重要反例,最后推导了T_(2(3/4))-分离型邻域空间与T_i(i=3(1/2),3,21/2(,2,1)-型邻域空间相互间的关系。     

一类n维自映射有异状点的充要条件

设f是可降的n维自映射,给出了这类自映射有异状点的一个充要条件.