Existence of horseshoe maps in voltage-mode controlled buck converters

In this paper, chaos in a voltage-mode controlled buck converter is studied. The existence of chaos is proven theoretically in this system. The proof consists of showing that the dynamics of the system is semiconjugate to that of a one-sided shift map, which implies positive entropy of the system and hence chaotic behaviour. The essential tool is the horseshoe hypotheses proposed by Kennedy and Yorke, which will be reviewed prior to the discussion of the main finding.     

Phase—Locking Dynamics in Coupled Circle—Map Lattices

The phase-locking dynamics in 1D and 2D lattices of non-identical coupled circle maps is explored.A global phase locking can be attained via a cascade of clustering processes with the increase of the coupling strength.Collective spatiotemporal dynamics is observed when a global phase locking is reached.Crisis-induced desynchronization is found,and its consequent spatiotemporal chaos is studied.     

Dynamics analysis on neural firing patterns by symbolic approach

Neural firing patterns are investigated by using symbolic dynamics. Bifurcation behaviour of the Hindmarsh--Rose (HR) neuronal model is simulated with the external stimuli gradually decreasing, and various firing activities with different topological structures are orderly numbered. Through constructing first-return maps of interspike intervals, all firing patterns are described and identified by symbolic expressions. On the basis of ordering rules of symbolic sequences, the corresponding relation between parameters and firing patterns is established, which will be helpful for encoding neural information. Moreover, using the operation rule of $\ast$ product, generation mechanisms and intrinsic configurations of periodic patterns can be distinguished in detail. Results show that the symbolic approach is a powerful tool to study neural firing activities. In particular, such a coarse-grained way can be generalized in neural electrophysiological experiments to extract much valuable information from complicated experimental data.     

A Non-symmetric Digital Image Secure Communication Scheme Based on Generalized Chaos Synchronization System

Based on a generalized chaos synchronization system and a discrete Sinai map, a non-symmetric true color （RGB） digital image secure communication scheme is proposed. The scheme first changes an ordinary RGB digital image with 8 bits into unrecognizable disorder codes and then transforms the disorder codes into an RGB digital image with 16 bits for transmitting. A receiver uses a non-symmetric key to verify the authentication of the received data origin, and decrypts the ciphertext. The scheme can encrypt and decz：Fpt most formatted digital RGB images recognized by computers, and recover the plaintext almost without any errors. The scheme is suitable to be applied in network image communications. The analysis of the key space, sensitivity of key parameters, and correlation of encrypted images imply that this scheme has sound security.     

Periodic solutions in one-dimensional coupled map lattices

IntroductionDynamicsofcoupledmaplattices (CML )haverecentlyattractedconsiderableattention[1- 4].IthasbeenfoundthatCMLsexhibitavarietyofspace_timepatterns:space_timeintermittency ,spatiotemporalchaos,frontsandinterfaces,nonlinearperiodicsolutions.Inthispaper,anone_dimensionalinfinitechainofnonlinearcoupledmapsisconsideredandtheexistenceofperiodicsolutionsisprovedwhenthecouplingstrengthαissmallenough .Ourapproachistheanti_integrablelimitintroducedinRefs.[5-7] .Intheanti_integrablelimit(coup…     

A Prelude Staircase to a Type V Intermittency in Two-Dimensional Discontinuous Maps

A sequence of periodic attractors has been observed in a two-dimensional discontinuous map, which canbe considered as a model of impact oscillator. The so-called "transfer number", which is defined as the mean numberof transfer from non-impact state to impact state per iteration, is locked onto a lot of rational values to form a curveconsisting of many steps. Our numerical investigation confirms that every step is confined by conditions created by thecollision between the periodic orbit and the discontinuous boundary of the system. After the last collision the systemshows a chaotic motion with intermittent characteristics. Therefore the staircase can be addressed as a "prelude staircaseto type V intermittency". The similar phenomenon has also been observed in a model of electric circuit. These resultsof our study suggest that this kind of staircases is common in two (or even higher) dimensional discontinuous maps.     

A control method for congested traffic in the coupled map car-following model

Based on the pioneer work of Konishi et al, a new control method is presented to suppress the traffic congestion in the coupled map (CM) car-following model under an open boundary. A control signal concluding the velocity differences of the two vehicles in front is put forward. The condition under which the traffic jam can be contained is analyzed. The results are compared with that presented by Konishi et al [Phys. Rev. 1999 E 60 4000--4007]. The simulation results show that the temporal behavior obtained by our method is better than that by the Konishi's et al. method, although both the methods could suppress the traffic jam. The simulation results are consistent with the theoretical analysis.     

抛物型非线性边界控制系统解映射的正则性

该文利用半群理论等方法讨论了抛物型非线性边界控制系统解映射的连续性、可微性     

曲面的第Φ_r-形式及无穷小等距

本文考虑光滑曲面片 M上的基本 Φr 形式及无穷小变形 Φ,推广了一些经典的结果 .主要有如下两个定理 :定理 A　若Φr=λΦ1或Φr+ 1=Φr 对某 r=2 ,3,…成立 ;或Φr=λΦq 对某 r>q≥ 1成立 ,则 M是全脐的或可展的 ,极小的 ,其中λ是 M上的函数 .定理 B　若Φ是无穷小Φr+ 1等距的 ( r>2 ) ,如果在 M上 :( a) K≠ 0 ,δK=0或 K >0 ,δH =0 ;( b)存在M上的函数λ,使δΦr=λΦr,则Φ也是无穷小Φr 等距的 .     

向量集值映射的共轭对偶

借助抽象算子将共轭映射的概念的到抽象空间,引入了集值映射的共轭映射和次梯度,据此讨论了集值映射共轭对偶的全局稳定性。