Numerical Simulations and Analysis of the Generalized Resource Budget Model in Ecology

• Main Authors: Wu, Kuan-Wei, 吳冠緯
• Other Authors: 張書銘
• Format: Others
• Language: en_US
• Published: 2012
• Online Access: http://ndltd.ncl.edu.tw/handle/32657503425707955361

碩士 === 國立交通大學 === 應用數學系所 === 100 === In our work, we use mathematical theorem and computer-assists to determine whether maps or systems are chaotic. We use topological entropy and lyapunov exponents, and use stability analysis to find the boundary of parameters that has periodic solution. If a system have positive topological entropy means that system is chaotic according to the definition of Li and Yorke and if system have positive Lyapunov exponent means sensitivity in Devaney's chaos. In ecology, Satake and Iwasa's generalized resource budget model that modified from Isagi et al.'s resource budget model in 2000. In this work, mathematical views and numerical analysis are presented to discover the sufficient condition that synchronicity will happened and to discover the conditions that the system have positive topological entropy and positive Lyapunov exponent on Satake and Iwasa's generalized resource budget model. Subsequently, topological entropy are utilized to prove that the model is chaotic in Li and Yorke's sense.