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Unpredictability of Iteration Destination in an Integrate-and-Fire Circuit

Chinese Physics Letters 2006年第8期23卷 2023-2026页

作者：戴俊胡进锟褚翔升何大韧 College of Physics Science and Technology Yangzhou University of China Yangzhou 225002 College of Mathematics and Physics Jiangsu University of Science and Technology of China Zhenjiang 212003 Institute of Physics Academia Sinica Taipei 11529

Based on our previous study that discovered a new mechanism of the riddled-like basin appearance in piecewise continuous and noninvertible links of two conservative mappings, and the mechanism being the mixing of different attraction basins on a fat-fractal set, which was addressed as the forbidden region net [Phys. Rev. E 72 （2005） 025201（R）], we show numerically that the riddled-like attraction basins and the new mechanism appear in an integrate-and-fire circuit that can be described by piecewise continuous and noninvertible links of two dissipative mappings. This leads to the fact that vast increase of the precision of the initial condition results in practically no improvement in predictability of the iteration destination. Predictability is usually characterized by examining how error probability in the prediction, f（ε）, scales with the precision ε under the initial condition. Typically, f（ε） - ε^α with 0 ≤ α ≤ 1 being the uncertainty exponent. For riddled-like basins, a should be zero, which is in good agreement with the numerical simulation results.

关键词： QUASI-DISSIPATIVE SYSTEM dynamical-systems ATTRACTORS CRISIS WEB

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Realization of Complete Synchronization between Different systems by Using Structure Adaptation

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Chinese Physics Letters 2006年第5期23卷 1118-1121页

作者：刘曾荣罗吉贵 The Shanghai University Center for Nonlinear Sciences Shanghai University Shanghai 200444 College of Science Shanghai University Shanghai 200444

We study the complete synchronization between different systems. Based on our new idea about structure adaptation, a new synchronized method, i.e. the structure adaptive method, is proposed. We believe that this self-adaptive mechanism correctly represents essential characteristics of self-adaptation in complex systems. We also show that this method is reasonable both from the coupling viewpoint in physics and from the controller design viewpoint in control theory.

关键词： CHAOTIC SYNCHRONIZATION dynamical-systems

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Lie Symmetries and Conserved Quantities for Super-Long Elastic Slender Rod

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Chinese Physics Letters 2007年第10期24卷 2773-2776页

作者：赵维加翁玉权傅景礼 Department of Mathematics Qingdao University Qingdao 266071 Institute of Mathematical Physics Zhejiang Sci-Tech University Hangzhou 310018 Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai 200072

DNA is a nucleic acid molecule with double-helical structures that are special symmetrical structures attracting great attention of numerous researchers. The super-long elastic slender rod, an important structural model of DNA and other long-train molecules, is a useful tool in analysing the symmetrical properties and the stabilities of DNA. We study the Lie symmetries of a super-long elastic slender rod by using the methods of infinitesimal transformation. Based on Kirchhoff＇s analogue, generalized Hamilton canonical equations are analysed. The infinitesimal transformations with respect to the radian coordinate, the generalized coordinate, and the quasimomentum of the model are introduced. The Lie symmetries and conserved quantities of the model are presented.

关键词： dynamical-systems POINT-SYMMETRIES

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