NCTS & NCU Spring Course in Mathematical Biology
Reaction-Diffusion Models and Bifurcation Theory

     Instructor: Junping Shi 史峻平
Email: junpingshi@gmail.com

Lecture place: Lecture Room B of National Center for Theoretical Sciences 4th Floor, The 3rd General Building, National Tsing Hua University
Lecture Time: Tuesday 2-5pm; Office Hours: Monday 3-5pm or by appointment (Office: NCTS 4th floor C20)
Course webpage: http://jxshix.people.wm.edu/2013-taiwan/course.htm

Lecture schedule

Day	Content	Slides	Homework	References	Software	Wiki
2/26	Basic and examples from ODEs	Lecture 1	Homework 1 solution	Noy-Meir Jour Ecology 1975 Solow Quart Jour Econ 1956 Scheffer Nature 2001 Rosenzweig 1971 Science Hsu 1978 Math Biosci Wang-Shi-Wei 2011 JMB Jiang-Shi 2009 book chapter	alpha pplane Matlab: pplane bifurcation	Bifurcation   Buckling Catastrophe theory Hopf bifurcation periodic orbit Routh-Hurwitz criterion
3/5	Models in growth and interaction	Lecture 2	Homework 2 solution	Sigmund review Tyson-Othmer, 1978 Eigen-Shuster, 1978 Angeli et.al. 2004 Craciun et.al. 2006	Matlab: logistic van der pol lorenz	Heinz von Foerster logistic equation Gompertz curve Hill function sigmoid function Michaelis–Menten Generalised logistic function Allee effect rate equation autocatalytic reaction Gierer-Meinhardt model self-organization Laozi hypercycle Quasispecies model origin of life Five elements (Chinese)
3/12	Diffusion and advection	Lecture 3	Homework 3 solution	Einstein 1905 (Brownian) Fisher 1937 Skellam 1951	Matlab: random walk  random walk 2d random walk 3d Brownian motion Binomial dis Normal dis heat eq 1 heat eq 2	vector calculus Laws of science Continuity equation Diffusion Molecular diffusion  diffusion coefficient Fick's law Fourier's law heat equation Laplace operator  random walk  Brownian motion binomial distribution    Normal Distribution error function Fisher's equation shape of drum
3/19	Numerical methods, cross-diffusion chemotaxis, nonlocal models	Lecture 4	Homework 4 solution	Keller-Segal,1970, 1971a, 1971b Shigesada et.al. 1979 Ni 1998 Hillen-Painter 2009 Hutson et.al 2003	Matlab: KPP Neumann KPP Dirichlet KPP advection Brusellator	Finite difference method Chemotaxis nonlocal equation
3/26	Stability in reaction-diffusion equations	Lecture 5	Homework 5 solution	Sweers 2000 Max. principle Matano 1979 Henry 1981, Smoller 1982		Banach space Compact operator Sobolev embedding maximum principle Schauder estimates
4/2	Stability of constant steady state	Lecture 6	Homework 6 solution	Turing 1952 Hsu 2005 TJM Yi-Wei-Shi 2009 JDE Zhao 2009 CAMQ		Gierer-Meinhardt model
4/9	Abstract bifurcation theory	Lecture 7	Homework 7 solution	Banach 1922 Hamilton 1982 BAMS Crandall-Raninowitz 1971 JFA Crandall-Raninowitz 1973 ARMA Shi 1999 JFA Liu-Shi-Wang 2007 JFA Liu-Shi-Wang 2013 JFA		contraction mapping theorem implicit function theorem Banach Banach manifold immersion submersion
4/16	Application of local bifurcation, Global bifurcation	Lecture 8	Homework 8 solution	Shi-Shivaji 2006 JMB Rabinowitz 1971 JFA Rabinowitz 1972 lecture notes Shi-Wang 2009 JDE		Mawhin 1999 review of LS degree
4/23	More Examples of Global bifurcation	Lecture 9	Homework 9 solution Arino et.al 2003	van den Driessche Watmough 2002, MB Wang-Zhao 2012 SIAM-ADS Wang-Liu-Shi-del Rio, 2013, JMB		Epidemic model basic reproduction number
4/30	Hopf bifurcation	Lecture 10	Homework 10 solution	Hopf, 1942 (English translation) Marsden-McCracken, 1976, book Crandall-Rabinowitz 1977 ARMA Alexander-Yorke 1978 AMJ Golubitsky-Rabinowitz comment		Hopf bifurcation periodic orbit E. Hopf
5/7	Delay differential equations	Lecture 11		Chen-Shi-Wei, 2013, JNS   Shi, 2013, survey paper Ruan 2006 survey paper   Smith 2011 book Mackey-Glass, 1977 Science Gurney et.al.1978, Nature		George Evelyn Hutchinson Mackey-Glass equation
5/14	Delayed reaction-diffusion equations	Lecture 12		Su-Wei-Shi, 2009, JDE  Su-Wei-Shi, 2012, JDDE Chen-Shi, 2012, JDE Atiyah 2011 Wang Yuan 2011		数学传播 数学文化 Michael Atiyah Cliff Taubes Yuan Wang