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-...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.展开更多
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 diff...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.展开更多
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 mod...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.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 10372054 and 70431002.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 10275053. C.-K. Hu and D.-R. He are also supported by the National Science Council in Taiwan under Grant No NSC 93-2112-M 001-027 and the National Center for Theoretical Sciences at Taipei： Physics Division.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant Nos 10672143 and 10472067, and the Natural Science Foundation of Henan Province under Grant No 0511022200.
文摘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.
