Hopf Bifurcation in A Biological Population with Disease Spread.

• Main Authors: Huang, Yu-Jen, 黃侑仁
• Other Authors: Cheng, Chang-Yuan
• Format: Others
• Language: zh-TW
• Published: 2014
• Online Access: http://ndltd.ncl.edu.tw/handle/59133153636378992677

碩士 === 國立屏東教育大學 === 應用數學系 === 102 === 　In this paper, we use theory in dynamical systems to investigate a biological problem. We modified the model mentioned in the literature, and used the Hopf bifurcation to study the biological population with disease spread in a predator-prey system. The factors are the maximum predation rate per predator per prey, the per capita growth rate of the prey when rare, the natural per capita death rate of the predator, the biomass conversion constant, the carrying capacity of the prey and the disease-induced per capita death rate of the predator. By changing the coefficient of disease transmission, we examine the existence of limited cycles in our model. Also, we find the equilibrium point and analyze the stability equilibrium by calculating the Jacobian matrixin. In order to confirm the theoretical result, we finally use Maxiam and Matlab programs to compare the simulation of our model and the numerical results.