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Global behavior of solutions to a class of second-order rational difference equations.

机译：一类二阶有理差分方程解的整体行为。

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For every choice of positive parameters alpha, beta, gamma, A, B and C, consider the two difference equations xn+1=a+bxn+g xn-1Z+Bxn+Cxn-1 ,n=0,1,2,...,x-1,x 0∈&sqbl0;0,infinity&parr0; E1 and xn+1=a+bxn+g xn-1Bxn+Cxn-1 ,n+0,1,2,...,x-1,x 0∈0,infinity, E2;In this thesis, it is shown that all solutions to Eqns.(E1) and (E2) converge to the positive equilibrium or to a prime period-two solution.;A complete qualitative description of the global behavior of solutions to (El) with nonnegative parameters is also given in this thesis whenever prime period-two solutions exist.;Furthermore, a relation is established between local stability of equilibria and slopes of critical curves of planar maps. Then this result is used to give global behavior for nonnegative solutions of the system of difference equations xn+1=b1xn 1+xn+c1yn +h1yn+1=b2 yn1+yn+c2xn +h2n=0,1,&ldots; ,x0,y0 ∈&sqbl0;0,infinity&parr0;x&sqbl0;0,infinity&parr0; with positive parameters. In particular, it is shown that the system has between one and three equilibria, and that the number of equilibria determines global behavior as follows: if there is only one equilibrium, then it is globally asymptotically stable. If there are two equilibria, then one is a local attractor and the other one is nonhyperbolic. If there are three equilibria, then they are linearly ordered in the south-east ordering of the plane, and consist of a local attractor, a saddle point, and another local attractor. In addition, sufficient conditions are given for the system to have a unique equilibrium.

机译：对于正参数alpha，β，γ，A，B和C的每种选择，请考虑两个差分方程xn + 1 = a + bxn + g xn-1Z + Bxn + Cxn-1，n = 0,1,2， ...，x-1，x0∈＆sqbl0; 0，infinity＆parr0; E1和xn + 1 = a + bxn + g xn-1Bxn + Cxn-1，n + 0,1,2，...，x-1，x0∈0，无穷大，E2;证明了方程（E1）和（E2）的所有解都收敛到正平衡或素数周期二解。;还给出了具有非负参数的（E1）的解的整体性质的完整定性描述。只要存在素数周期为两个的解，就可以得出本论文的结论。此外，还建立了平衡点的局部稳定性与平面图的临界曲线的斜率之间的关系。然后，该结果用于给出差分方程组xn + 1 = b1xn 1 + xn + c1yn + h1yn + 1 = b2 yn1 + yn + c2xn + h2n = 0,1，l的非负解的全局行为。，x0，y0∈＆sqbl0; 0，infinity＆parr0; x＆sqbl0; 0，infinity＆parr0;具有正参数。特别是，它表明系统具有一到三个平衡点，并且平衡点的数量决定了全局行为，如下所示：如果只有一个平衡点，则它是全局渐近稳定的。如果存在两个均衡，则一个是局部吸引子，另一个是非双曲线的。如果存在三个平衡点，则它们按平面的东南顺序线性排列，并由一个局部吸引子，一个鞍点和另一个局部吸引子组成。另外，给出了足以使系统具有唯一平衡的条件。

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作者
Basu, Sukanya.;
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作者单位

University of Rhode Island.;

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授予单位 University of Rhode Island.;
学科 Mathematics.
学位 Ph.D.
年度 2009
页码 111 p.
总页数 111
原文格式 PDF
正文语种 eng
中图分类数学;
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专利

1. Global Behavior of Solutions to Two Classes of Second-Order Rational Difference Equations [J] . Sukanya Basu, Orlando Merino Advances in Difference Equations . 2009,第1期

机译：两类二阶有理差分方程解的整体性质
2. Global behaviour of solutions to a class of second-order rational difference equations when prime period-two solutions exist [J] . Basu S. Journal of difference equations and applications . 2013,第5a6期

机译：存在素数周期二解时一类二阶有理差分方程解的整体性质
3. Global Solutions and Periodic Solutions for a Second-Order Quadratic Rational Difference Equation [J] . International Journal of Difference Equations . 2016,第1期

机译：二阶二次有理差分方程的整体解和周期解
4. Existence of Periodic Solutions for a Class of Second-order Nonlinear Difference Systems [C] . Tan Weiming, Sufang International conference on mechanical engineering, materials and energy . 2012

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7. Decision-making is the process of analyzing information about a problem situation and comparing it to a specific conclusion in order to solve a specific problematic (Yıkılmaz, 2001; Miller and Byrnes, 2001). Decision-making styles are a mechanism that is influenced by the internal and external conditions that determine the direction of the decisions of the individual, the content of the decision-making process, and the outcome of the decision-making process (Payne, Bettman and Johson, 1993; Bavol’ár and Orosová, 2015). ACT is a contemporary member of the Cognitive Behavioral Therapy family. ACT (Acceptance and commitment therapy) has both similar and different directions with Behavioral Therapies and Cognitive Therapies (Herbet and Forman, 2011; Hayes, 2004). KKT responds to classical behavioral treatments using both existential and cognitive approaches in the analysis of behavior. KKT is a science wing that tries to solve human problems with a wider perspective aimed at solving problematic human behaviors (Plumb, Stewart, Dahl and Lundgren, 2009). It is seen that there is very little research about the new approach of ACT approach when the aiming country of our country is screened and it is thought that our country will contribute to the field of psychological counseling with the work done. In the scope of the research, experimental and control groups and preliminary test, post-test and follow-up measurements of 2x3 experimental design were used. The study's study group consists of a total of 24 (12 experimental and 12 control groups) university students studying in different departments and levels, continuing their education in the academic year of 2015-2016 in Ağrı province and İbrahim Chechen University in 2015-2016 academic year. The average age of participants in the experiment and control group is 20. There were 12 participants in the experimental group, 7 female and 5 male, and 12 participants, 7 female and 5 male in the control group. Personal Information Form and Decision Making Style Scale prepared by the researcher were used in the research. In order to decide on the tests to be used in the course of analyzing the data, the scores of the participant's Decision Styles Scale pre-test, which are placed primarily in the experimental and control groups, it was analyzed whether the basic expectations of parametric tests were answered. As a result of the analysis made, the scores, skewness and kurtosis coefficients obtained from the Decision Making Styles Scale were given to the experimental and control groups. It was determined that the distribution was normal in the result of Shapiro-Wilk test, in which the skewness and kurtosis coefficients of each sub-scale were ranked between -1 and +1. 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机译：决策是分析有关问题情况的信息并将其与特定结论进行比较的过程，以解决特定的问题（Yıkılmaz，2001; Miller和Byrnes，2001）。决策风格是一种机制，受到内部和外部条件的影响，确定个人决定的方向，决策过程的内容以及决策过程的结果（PAYNE，BETTMAN和BEDNE） Johson，1993;Bavol'ár和奥萨洛瓦，2015）。法案是认知行为治疗家庭的当代成员。行为（验收和承诺治疗）具有与行为疗法和认知疗法的类似和不同方向（Herbet和Forman，2011; Hayes，2004）。 KKT在分析行为中使用存在性和认知方法来响应古典行为治疗方法。 KKT是一个科学翼，试图解决人类问题，旨在解决有问题的人类行为（铅垂，斯图尔特，Dahl和Lundgren，2009）。有人认为，当我们国家的瞄准国家进行筛选时，有关行动方法的新方法几乎没有研究，并且认为我们的国家将为完成工作做出贡献的心理咨询领域。在研究的范围内，使用实验和对照组和初步测试，使用后测试和后续测量的2x3实验设计。该研究的研究小组包括共24名（12个实验和12个对照组）大学学生在不同的部门和水平上学习，在2015-2016学术上继续进行2015-2016的学术年度2015-2016学年年。实验和对照组参与者的平均年龄是20.实验组中有12名参与者，7名女性和5名男性，12名参与者，7名女性和5名男性。研究人员准备的个人信息表格和决策制定风格规模在研究中使用。为了决定在分析数据的过程中使用的测试，参与者的决策风格刻度预测的分数主要在实验和对照组中进行，分析了参数的基本期望吗？测试得到了回答。由于对实验和对照组给出了从决策曲调标度获得的分数，偏移和峰度分子系数。确定该分布是正常的在成熟的-WILK试验结果中，其中每亚级的偏差和刚度系数在-1到+1之间排名。实验和对照组的参与者;决策式预测测量的同质性测试结果表明数据是均匀的。根据毛毛环保试验的结果，已确定工作支持假设。据确定，从依赖决策风格的实验和对照组获得的预测分数之间没有显着差异，但测试组在测试后的分数内显示出较低的平均分数和后续的分数 - 测试。因此，可以说，应用于实验组的面向活动的心理教育程序减少了决策风格子维度的依赖决策风格分数，并且心理教育程序具有持久的效果。据确定，从实验和对照组自发决策风格获得的预测试，测试后和后续评分之间没有显着差异。因此，可以说这种情况不会导致从应用于实验组的活动导向的心理教育程序的决策风格分数的自发决策风格分数显着差异。行为的心理教育计划在个人直观的决策风格下降，但这种减少并没有产生显着的差异。因此，可以说，这种情况不会在从应用于实验组的KKT导向的心理教育程序的决策风格分数中产生有意义的决策风格分数。从实验和对照组的理性决策风格获得的预测分数显示后检验后和随访评分之间存在差异，但这种差异并不重要。由于分析，确定测试组的理性决策风格较高，而不是后测试和后续分数的预测分数，而对照组合理决策风格的后测试和后续测试分数显示出与预测试分数相比的减少。预测分数。决策款式扩展避免决策由于分析了预测试，测试后和后续措施的班次评分的平均分数，发现群体效应是微不足道的。确定实验和对照组从避免决策风格获得的预测评分中显着不同，但在测试后和后续测试的分数内没有显示出任何重大变化。

Global behavior of solutions to a class of second-order rational difference equations.

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