Mathematical Structure for Forest Bynamics with Interaction between Trees and Soils

树木与土壤相互作用的森林动力学数学结构

• 批准号: 16340046
• 负责人: YAGI Atsushi
• 金额: $ 5.3万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2004
• 资助国家: 日本
• 起止时间: 2004 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-16340046/
• 关键词: Forest kinematic model; Nonlinear differential equations; Dynamical system; Self-orvanization; Numerical simulation; Forest boundary; 自己組織化現象; 計算数学

We are concerned with the dynamics of forest system. Considering the system as a hybrid system of trees and soils with some interactions, we introduced a mathematical model which describes the kinetics of system. The model is expressed by a system of nonlinear partial differential equations. In this research program we have studied analytically and numerically the model mainly in a case where the soil level is constant and stable. In such a case we constructed a dynamical system determined from the model equations, constructed a Iyapunov function for the dynamical system, showed that every trajectory converges asymptotically to a stationary solution and clarified that the structure of equilibria, i.e., stationary solutions of model equations, changes drastically depending on the various parameters in the equations which represent the state of the forest. Furthermore we have found out that this model gives us a clear boundary which may seem to correspond to the forest boundary which the forest possesses inherently: This means that observing the best boundary we can inversely identify all the parameters in the model to know the mathematical structure of the forest system. This suggests, furthermore, that it is possible in the future to know from observations of the bust boundary the degree of health or the power of restitution from destruction for the forest itself. As for the case where the soil level is non constant and unstable, we have only performed numerical simulations. We found out some interesting quasi-periodic trajectories. But the mathematical analysis remains to be studied in the future.

我们关心的是森林系统的动态。将该系统看作是一个具有相互作用的树木和土壤的混合系统，建立了描述系统动力学的数学模型。该模型由一个非线性偏微分方程组表示。在本研究计划中，我们分析和数值研究的模式，主要是在土壤水平是常数和稳定的情况下。在这种情况下，我们构造了一个由模型方程确定的动力系统，构造了动力系统的Iyapunov函数，证明了每个轨迹渐近收敛到一个稳态解，并阐明了平衡点的结构，即，模型方程的静态解，根据代表森林状态的方程中的各种参数而急剧变化。此外，我们还发现，这个模型给了我们一个清晰的边界，似乎对应于森林固有的森林边界：这意味着，观察最佳边界，我们可以反向识别模型中的所有参数，以了解森林系统的数学结构。这进一步表明，将来有可能从对森林破坏边界的观察中了解森林本身的健康程度或从破坏中恢复的能力。对于土层高度不稳定的情况，我们只进行了数值模拟。我们发现了一些有趣的准周期轨迹。但其数学分析还有待于进一步研究。

项目成果

On the solvability of complete abstract differential equations of elliptic type

椭圆型完全抽象微分方程的可解性

• 发表时间: 2004
• 期刊: Funkcialaj Ekvacioj 47・2
• 作者: Y.Giga;S.Matsui;S.Sasayama;早川貴之;Seiichiro Wakabayashi;早川貴之;Tatsuro Ito;Atsushi Yagi
• 通讯作者: Atsushi Yagi

Asymptotic Behavior of Solutions for Forest Kinematic Model

• DOI: 10.1619/fesi.49.427
• 发表时间: 2006
• 作者: L. Chuan;T. Tsujikawa;A. Yagi

w-limit sets of dynamical system for forest kinematic model

森林运动模型动力系统的w极限集

• 发表时间: 2006
• 作者: L. H.;Chuan;et. al.
• 通讯作者: et. al.

Asymptotic behavior of solutions for forest kinematic model under Dirichlet conditions

狄利克雷条件下森林运动模型解的渐近行为

• 发表时间: 2007
• 期刊: Scientiae Mathematicae Japonicae 66-2
• 作者: J-S. Hwang;S. Nakagiri;K.Kuwae;高桑 昇一郎;S. Haruki;倉田 和浩;桑江一洋;J-S. Hwang;赤穂まなぶ;石渡聡;S. Nakagiri;桑江一洋;赤穂まなぶ;高桑昇一郎;S. Nakagiri;塩谷隆;平田雅樹;Y. Takei;石渡聡;平田雅樹;T. Shirai;桑江一洋;倉田和浩;T. Shirai
• 通讯作者: T. Shirai

Optimal control for an adsorbate-induced phase transition model

吸附物诱导相变模型的优化控制

• 发表时间: 2005
• 期刊: Applied Math.Comput. 171巻
• 作者: S.-U.Ryu;A.Yagi
• 通讯作者: A.Yagi