學術活動
Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in arid environments
2009-06-17
來源：科技處 點擊次數：主講人：Jonathan Sherratt 教授（Department of Mathematics, Heriot-Watt University,UK）
时 间： 6月19（星期五）下昼15：30-16：30
地 点： 數學科學學院211 课堂
主 办： 數學科學學院
摘 要： In many semi-arid environments,vegetation is self-organised into spatial patterns.The most striking examples of this are on gentle slopes,where striped patterns are typical,running parallel to the contours.I will discuss pattern solutions of a mathematical model for this phenomenon,of reaction-diffusion-advection type.
I will describe the use of numerical bifurcation methods of both the pattern odes and a discretised version of the model pdes.I will show that patterns exist for a wide range of rainfall levels.Moreover,for many rainfall levels,patterns with a variety of different wavelengths are stable,with mode selection dependent on initial conditions.This raises the possibility of hysteresis,and I will present numerical solutions of the model which show that pattern selection depends on rainfall history in a relatively simple way.
