通讯机构：
[Huang, Chuangxia] C;Changsha Univ Sci & Technol, Sch Math & Stat, Hunan Prov Key Lab Math Modeling & Anal Engn, Changsha 410114, Hunan, Peoples R China.
关键词：
Nicholson-type system;global attractivity;patch structure;asymptotically almost periodic solution
摘要：
<jats:p>In this article we study a delayed Nicholson-type system involving patch structure. We apply differential inequality techniques to establish a sufficient condition for the existence of positive asymptotically almost periodic solutions. By constructing suitable Lyapunov functions, we obtain a new criterion for the uniqueness and global attractivity of the asymptotically almost periodic solutions.
For more information see https://ejde.math.txstate.edu/Volumes/2020/61/abstr.html</jats:p>
作者机构：
[Huang, Lihong; Wang, Jiafu; Wang, JF; Huang, LH; Huang, Chuangxia] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Wang, Jiafu] Cent South Univ Forestry & Technol, Inst Math & Phys, Changsha 410004, Hunan, Peoples R China.
通讯机构：
[Wang, JF; Huang, LH] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
关键词：
Convergence of numerical methods;Linear systems;Canonical form;Discontinuity;Existence and stability;Limit-cycle;Parameter regions;Parameter spaces;Piece-wise linear systems;Piecewise linear differential systems;Piecewise linear techniques
期刊：
Journal of Mathematical Analysis and Applications,2019年469(1):405-427 ISSN：0022-247X
通讯作者：
Wang, Jiafu
作者机构：
[Huang, Lihong; Wang, Jiafu] Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.;[Chen, Xiaoyan] Cent South Univ Forestry & Technol, Inst Math & Phys, Changsha 410004, Hunan, Peoples R China.
通讯机构：
[Wang, Jiafu] C;Changsha Univ Sci & Technol, Sch Math & Stat, Changsha 410114, Hunan, Peoples R China.
关键词：
Limit cycle;Poincare-Bendixon theorem;Stability;Piecewise linear differential systems
摘要：
The objective of this paper is to study the number and stability of limit cycles for planar piecewise linear (PWL) systems of node-saddle type with two linear regions. Firstly, we give a thorough analysis of limit cycles for Lienard PWL systems of this type, proving one is the maximum number of limit cycles and obtaining necessary and sufficient conditions for the existence and stability of a unique limit cycle. These conditions can be easily verified directly according to the parameters in the systems, and play an important role in giving birth to two limit cycles for general PWL systems. In this step, the tool of a Bendixon-like theorem is successfully employed to derive the existence of a limit cycle. Secondly, making use of the results gained in the first step, we obtain parameter regions where the general PWL systems have at least one, at least two and no limit cycles respectively. In addition for the general PWL systems, some sufficient conditions are presented for the existence and stability of a unique one and exactly two limit cycles respectively. Finally, some numerical examples are given to illustrate the results and especially to show the existence and stability of two nested limit cycles. (C) 2018 Elsevier Inc. All rights reserved.
通讯机构：
[Tong, Xiaojiao] C;Changsha Univ Sci & Technol, Coll Math & Comp Sci, Changsha 410076, Hunan, Peoples R China.
会议名称：
2007 IEEE Power Engineering Society General Meeting
会议时间：
June 2007
会议地点：
Tampa, FL, USA
会议论文集名称：
2007 IEEE Power Engineering Society General Meeting
关键词：
Power market;Dynamic bidding model;Nash equilibrium;Bounded constraints
摘要：
A dynamic bidding model of power markets is presented in this paper. The new model is composed of a difference dynamic system and the bounded constraints of bidding variables. The remarkable characteristics of the model include: (i) it adopts a process of dynamic adjustment bid where the limit point is the Nash equilibrium point; (ii) the transmission constraints of the network are considered; (iii) the bound of the bidding variables is involved. A numerical simulation is also presented to test the model's behaviors, including the convergence, the stability, and the relationship between the stability and parameters, respectively. The simulating results show that the new model is valid.
关键词：
Carbon;Electronic density of states;Electronic structure;Spectroscopic analysis;Energy graphene approximation;Fermi level;Normalized differential conductivity;Single walled carbon nanotubes;Nanotubes
摘要：
The analytical expression of the electronic density of states (DOS) for single-walled carbon nanotubes (SWNTs) has been derived on the basis of graphene approximation of the energy E(k) near the Fermi level EF. The distinctive properties of the DOS for SWNTs, the normalized differential conductivity and the current vs bias are deduced and analyzed theoretically. The singularities in the DOS (or in the normalized differential conductivity) predict that the jump structure of current (or conductance)-bias of SWNTs exists. All the conclusions from the theoretical analysis are in good agreement with the experimental results of SWNTs electronic structure and electronic transport. In other words, the simple theoretical model in this paper can be applied to understand a range of spectroscopic and other measurement data related to the DOS of SWNTs.
