| 日期 |
时间(上午) |
内容 |
时间(下午) |
内容 |
| 5/21(四) |
9-11 |
没有课 | 2-5 |
Darwin, Genetics,
Hardy-Weinberger law, Differential/difference
equations, bifurcation, stability,, biological models
(1-D), bistability, hysteresis, Matlab,
Differential/difference equations, bifurcation of maps, phase portrait
(Dfield), linear algebra(eigenvalue/eigenvector), 生物数学综述(pdf)
Fisher方程的由来
(ppt) |
| 5/22(五) |
9-11 |
Systems of equations,
phase portrait, competition, predator-prey models,
nondimensionalization, phase plane analysis, Poincare-Bendixson
theory, Pplane |
2-5 |
Bifurcation in competition, predator-prey models, paradox of enrichment, competition exclusion, Lyapunov functional, limit cycles, Hopf bifurcation, relaxation oscialltion, limit cycle, bifurcation/continuation, higher-dimensional models (competition, food-chain, etc), MatCont, 神经传导的方程 (pdf) 神经传导(中文科普)(pdf) Age structure model(pdf) |
| 5/23(六) |
休息 | 休息 | ||
| 5/24(周日) |
9-11 |
Diffusion, random walk, linear diffusion equation, eigenvalue problems, Fourier series, fundamental solutions, Fisher equation, traveling wave, minimal patch size, biological invasion, simulation of diffusion equations in Maple | Mississippi Bifurcation Lecture 1, Lecture 2, Lecture 3 |
|
| 5/25(一) |
9-11 |
Reaction-diffusion systems in
biology, chemistry, and physics, linearization/stability, Turing
instability, Hopf bifurcation, Numerical schemes, discrete diffusion
model/patch model, Survey Paper on Frontier of Math in China |
2-4 |
PDE Matlab solver,
numerical solutions of R-D systems PDE in Matlab by P. Howard |
| 5/26(二) |
9-11 |
Implicit function theorem, Bifurcation theory in infinite dimensional space, Sobolev/Holder spaces, Fisher equation, competition, predator-prey models, | ||
| 5/27(三) |
9-11 |
休息 | 休息 | |
| 5/28(四) |
9-11 |
Maximum principle, a priori
estimates, Degree theory, application of degree theory, global
bifurcation theorem |
||
| 5/29(五) |
9-11 |
Variational/energy methods,
Lyapunov functional, Hamiltonian systems, Gradient systems, Dissapative
systems |
||
| 5/30(六) |
9-11 |
Dynamical system approach
(monotone dynamical system) |