摘要：
Since bifurcation makes it difficult to manage a paddy ecosystem, controlling bifurcation is an important management tool. In this paper, the stability and bifurcation control for a fractional order paddy ecosystem in the fallow season with time delay are investigated. Firstly, a paddy ecosystem model formulated by two-dimensional delayed fractional order differential equations with linear delayed feedback controller is proposed to reveal the interaction between weeds and inorganic fertilizers in paddy systems. Using the time delay as the bifurcation parameter, the sufficient conditions for stability of the system and the existence of Hopf bifurcation are obtained by analyzing the relevant characteristic equations. The results show that the time delay can heavily affect the dynamics of the system, and the feedback gain and the fractional order have significant impact on the control effect. Finally, the verification of the accuracy and validity of these conclusions is made by two examples, the control effect of the feedback gain and the fractional order on Hopf bifurcation are illustrated intuitively by a contour map.
摘要：
By introducing a delayed fractional-order differential equation model, we deal with the dynamics of the stability and Hopf bifurcation of a paddy ecosystem with three main components: rice, weeds, and inorganic fertilizer. In the system, there exists an equilibrium for rice and weeds extinction and an equilibrium for rice extinction or weeds extinction. We obtain sufficient conditions for the stability and Hopf bifurcation by analyzing their characteristic equation. Some numerical simulations validate our theoretical results.
摘要：
Abstract: The sufficient conditions are obtained that the f(x) is a periodic function with period 2T, 3T or 4T for the functional equation f(x+T)f(x) =af(x+T)+bf(x)+c. The results generalize the existing conclusions.#@#@#摘要: 本文针对函数方程f(x+T)f(x) =af(x+T)+bf(x)+c分别获得f(x)是周期为2T、3T、4T函数的充分条件，推广了已有结论。
关键词：
This paper focuses on the multidirectional associative memory (MAM) neural networks with m fields which is more advanced to realize associative memory. Based on the Brouwer fixed point theorem and Dini upper right derivative;it is confirmed that the multidirectional associative memory neural network can have 3l equilibria and 2l equilibria of them are stable;where l is a parameter associated with the number of neurons. Furthermore;an example is given to illustrate the effectiveness of the results. Published: 2013 First available in Project Euclid: 14 March 2014 zbMATH: 06950768 MathSciNet: MR3138931 Digital Object Identifier: 10.1155/2013/592056
期刊：
Proceedings 2010 IEEE 5th International Conference on Bio-Inspired Computing: Theories and Applications, BIC-TA 2010,2010年:6-10
通讯作者：
Zhou, T.(tj_zhou@hunau.net)
作者机构：
[Tiejun Zhou; Haiquan Fang; Ming Wang] College of Science, Hunan Agricultural University, Changsha, Hunan 410128, China;[Tiejun Zhou; Xiaoqun Li] College of Orient Science and Technology, Hunan Agricultural University, Changsha, Hunan 410128, China
会议名称：
2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA)
会议时间：
September 2010
会议地点：
Changsha
会议论文集名称：
2010 IEEE Fifth International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA)
摘要：
By extending the bidirectional associative memory neural network model, a mathematical model of multidirectional associative memory (MAM) neural networks with constant time delays is proposed. By using Brouwer fixed point theorem and the upper right Dini derivative, a sufficient condition for the existence and the global exponential stability of an equilibrium point is obtained. And for a special MAM neural network which connection weights is positive, a sufficient and necessary condition for the existence and the global exponential stability of an equilibrium point is obtained. The results are new for MAM neural networks. An example and its numerical simulation are given to illustrate the effectiveness of the obtained results.
摘要：
Accurate prediction of genes in genomes has always been a challenging task for bioinformaticians and computational biologists. Therefore, the discovery of relations in coding and non-coding sequences has led to new perspectives in the understanding of the DNA sequences. This has motivated us to find new methods to distinguish coding and non-coding sequences. We first introduce a number sequence representation of DNA sequences. Multi-affinity analysis and local Hölder exponent are then performed on the representation of the obtained number sequence. Three suited exponents are selected to form a parameter space. The two exponents γ(-2), γ(6) are from Multi-affinity analysis, the exponent h is from local Hölder exponent. Thus, each coding or non-coding sequence may be represented by a point in the three-dimensional parameter space. We can see the points corresponding to coding and non-coding sequences in the complete genome of many prokaryotes be divided to different regions roughly. If the point (γ(-2), γ(6), h) for a DNA sequence is situated in the region corresponding to coding sequences, the sequence is discriminated as a coding sequence; otherwise, the sequence is classified as a non-coding one. Therefore these exponents can be used to distinguish coding and non-coding sequences. The Fisher's discriminant algorithm is used to give the discriminant accuracies. The average discriminant accuracies p<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub>, p<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nc</sub>, q<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">c</sub> and q<sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nc</sub> of all 51 prokaryotes obtained by the present method reach 69.08%, 83.34%, 72.08% and 83.54%, respectively.
