生態學中隨機及確定性網路的耦合網格

Abstract

在這篇論文中,我們考慮生態學中由隨機及確定性網路混合的耦合網格。此確定性網路的耦合網格是由 Isage 等人以及 Satake 和 Iwasa 建構自然森林中的同步繁殖過程的模型，並且也有統計及數值上的模擬。我們的模型包括了d，β，epsilon，r以及N這些參數，分別表示單棵樹能量衰退係數，確定性網路的本質耦合強度，隨機性網路的耦合強度，花粉傳播的半徑，以及樹的數量。這篇論文中我們有以下三個結果。第一，我們研究了這個模型在同步流型上的動態。當某些參數變動時，週期增加分歧，混沌動態以及全局吸引軌道會被識別出來。第二，我們研究了在兩顆樹情形時，此模型的全局同步。我們也導出一個此模型的”弱”Sharkovskii 排序。最後，我們得到了此模型局部同步的一些充分條件。

In this thesis, we consider two dimensional and nonsmooth coupled map lattices (CMLs) in ecology with a mixed type of deterministic and stochastic networks. The version of the corresponding CMLs with a deterministic network is proposed by Isage et al. and Satake and Iwasa to model the synchronized reproduction of a mature forest, where statistical and numerical simulations were provided. Our model contains parameters d, β, epsilon, r and N, representing the energy depletion coefficient of a tree, the intrinsic coupling strength of the deterministic network, the coupling strength of the stochastic network, the radius of pollen spread, and the number of trees, respectively. The following three main results are obtained. First, we study the dynamics of the model on its synchronized manifold. Period adding bifurcation, chaotic dynamics and globally attracting periodic orbits are identified as a certain parameters are varied. Second, we study the global synchronization of the model with two trees. We also derive a ”weak” Sharkovskii ordering for the two-dimensional map associated with the two-tree model. Finally, we obtain some sufficient conditions for the local synchronization of the model.