Chaos and Bifurcation of Piecewise Smooth Maps Arising in Ecology

• Main Authors: Deng, Ren-Yi, 鄧仁益
• Other Authors: Juang, Jonq
• Format: Others
• Language: zh-TW
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/72004127485496598938

碩士 === 國立交通大學 === 應用數學系所 === 101 === 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.