出現在生物學中分段光滑映射之混沌與分岔

Abstract

本論文包含兩個部分。在第一部分中，我們考慮一個廣義生 態資源預算模型，有一個參數d，是由一匝、沙他和岩 佐的資源模型預算來的。這裡的d 是耗盡係數。張書銘 藉由拓撲商是正的當ｄ>1.00026 來證明該模型有德瓦尼 的混亂在不變的集合上。我們改進了他們的結果藉由此模型 有正的拓撲商當ｄ>1。在第二部分，我們研究了路徑到混亂 的另一個分段光滑映射，此映射是由一匝、沙他和岩佐同步的森林模型來的。 這樣的映射包含兩個參數d和beta。這 裡的beta是指樹跟樹之間的交配花粉可用性的耦合強度。這是 透過數值展現，這種分段光滑映射路徑到混亂是通過有限的 兩倍週期分岔。我們藉由提供了幾個應用上的例子去進一步 說明這種路徑到混亂是通用的對於分段光滑映射。

This thesis contains two parts. In the first part, we consider a generalized resource budget model of ecology with a parameter d, which was modified from Isagi resource budget model by Staka and Iwasa. Here d is the depletion coefficient. Shu-Ming Chang thoutht that the model was shown that the model has Devaney 's chaos on an invariant set by proving its topological entropy is positive for d > 1.00026. We improve their result by proving that the map had positive topological entropy for d > 1. In this second part, we study the route to chaos for another piecewise smooth map, which governs the synchronized dynamics of the forest model of Isagi-Staka-Iwasa. Such map contains two parameters d and beta. Here beta denotes the coupling strength among the trees in their outcross pollen availability. It is numerically demonstrate that the route to chaos of such piecewise smooth map is through finite period doubling bifurcation. We further illustrate such route to chaos is generic for piecewise smooth maps by providing several examples arising in application.