Research on comparisons of Global Properties of solutions of Non-linear Difference Equations and solutions of Nonlinear Phenomena.

非线性差分方程解与非线性现象解的全局性质比较研究。

基本信息

批准号：
15540217
负责人：
SUZUKI Mami
金额：
$ 1.98万
依托单位：
Aichi-gakusen University
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2003
资助国家：
日本
起止时间：
2003 至 2005
项目状态：
已结题

项目摘要

1.There is no general existence theorem for solutions for nonlinear difference equations, so we must prove the existence of solutions in accordance with models one by one. In our work, we found theorems for the existence of analytic solutions of nonlinear second order difference equations.2.One of the main work of this research is obtaining representations of analytic general solutions which converge to an equilibrium point of nonlinear second order difference equations with new methods of complex analysis.3.For analytic solutions of a nonlinear first order difference equation, T.Kimura studied the cases in which eigenvalue equal to 1,furthermore N.Yanagihara studied the cases in which the absolute value of the eigenvalue equal to 1. For nonlinear second order difference equation in which the absolute values of the all eigenvalues equal to 1, we consider analytic solutions of it in this study.4.Furthermore we apply the our theory of nonlinear higher order difference equations to Dynamics of Economic systems, for example, Nonlinear Cournot Dynamics with Heterogenous Duopolists. Generally, economist consider only equilibrium points for Mathematical Models. They call the equilibrium points as "solution of the model", and ignore orbits of the true solutions of the Models. However the equilibrium points are not "solution" in mathematical means, furthermore the orbits are important in the systems. Therefore in this study, we derive the true solutions and represent of solutions of Cournot Dynamics.5.In other studies, we treat economic Models with time delay. One of them is a dynamic economic model in isolated island. This Model is nonlinear differential equation with delayed terms, and studied stability of it. Next we treat an singular perturbation problem for economic models of R.Goodwin.

1.对于非线性差异方程的解决方案的解决方案没有一般存在的定理，因此我们必须根据模型一一证明解决方案的存在。 In our work, we found theorems for the existence of analytic solutions of nonlinear second order difference equations.2.One of the main work of this research is obtaining representations of analytic general solutions which converge to an equilibrium point of nonlinear second order difference equations with new methods of complex analysis.3.For analytic solutions of a nonlinear first order difference equation, T.Kimura studied the cases in which eigenvalue equal to 1，此外，N.Yanagihara还研究了特征值的绝对价值等于1。对于非线性二阶差差方程，所有特征值的绝对值等于1，我们在这项研究中考虑了IT的分析解决方案。双重垄断主义者。通常，经济学家仅考虑数学模型的平衡点。他们将平衡点称为“模型的解”，而忽略了模型的真实解决方案的轨道。但是，在数学手段中，平衡点不是“解决方案”，此外，轨道在系统中很重要。因此，在这项研究中，我们得出了真正的解决方案，并代表了Cournot Dynamics的解决方案。5。在其他研究中，我们会随时间延迟处理经济模型。其中之一是孤立岛屿的动态经济模式。该模型是具有延迟项的非线性微分方程，并研究了其稳定性。接下来，我们将R.Goodwin的经济模型处理一个单一的扰动问题。