生物学里头都那些地方用到常微分方程组？

orionsnow

最近在做一个东西，要用常微分方程组。

想看看在生物里头哪里有应用，正好一边学习生物一边复习数学。

以前学数学建模好像有个 地中海鲨鱼的数量和鱼群的数量 可以用微分方程来描述。

另外就是药代动力学？ 不过好像有点远了。

johndoe

布朗运动。。。 随机微分转换为偏微分，然后求解。。。

orionsnow

5.1  传染病模型
5.2  经济增长模型
5.3  正规战与游击战
5.4  药物在体内的分布与排除
5.5  香烟过滤嘴的作用
5.6    人口预测和控制
5.7  烟雾的扩散与消失
5.8    万有引力定律的发现

daydayup009

计算神经科学，基本上都是从常微分方程描述的规则来推导各种模型的特性的。

orionsnow

http://www.math.rutgers.edu/~son ... gy_intro_ver1.1.pdf

http://www.math.rutgers.edu/~sontag/336/notes_biomath.pdf

http://www.math.rutgers.edu/~sontag/336.html



Modelling Differential Equations in Biology
2nd Edition
C. H. Taubes
Harvard University, Massachusetts
Paperback

(ISBN-13: 9780521708432)

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Based on a very successful one-semester course taught at Harvard, this text teaches students in the life sciences how to use differential equations to help their research. It needs only a semester's background in calculus. Ideas from linear algebra and partial differential equations that are most useful to the life sciences are introduced as needed, and in the context of life science applications, are drawn from real, published papers. It also teaches students how to recognize when differential equations can help focus research. A course taught with this book can replace the standard course in multivariable calculus that is more usually suited to engineers and physicists.

• Brought alive by reprints of recent research summary articles from Science and Nature illustrating the mathematics and demonstrating to students how the mathematics in the text is used by working biologists • Commentary for each reprinted article summarizes the underlying biological issues so neither students nor instructors need prior knowledge, and shows where and how the mathematics is used • Provides students with the mathematics that is commonly used by biologists and life scientists as opposed to the mathematics of physicists and engineers commonly found in other texts
Contents

1. Introduction; 2. Exponential growth with appendix on Taylor's theorem; 3. Introduction to differential equations; 4. Stability in a one component system; 5. Systems of first order differential equations; 6. Phase plane analysis; 7. Introduction to vectors; 8. Equilibrium in two component, linear systems; 9. Stability in non-linear systems; 10. Non-linear stability again; 11. Matrix notation; 12. Remarks about Australian predators; 13. Introduction to advection; 14. Diffusion equations; 15. Two key properties of the advection and diffusion equations; 16. The no trawling zone; 17. Separation of variables; 18. The diffusion equation and pattern formation; 19. Stability criteria; 20. Summary of advection and diffusion; 21. Traveling waves; 22. Traveling wave velocities; 23. Periodic solutions; 24. Fast and slow; 25. Estimating elapsed time; 26. Switches; 27. Testing for periodicity; 28. Causes of chaos; Extra exercises and solutions; Index.
Review

'Graduates of this course will be prepared to discuss the setup and structure of the underlying model, and to engage with the type of predictions that it can make. That's an admirable accomplishment for a book at this level! Moreover, equipping undergraduates with such a toolkit can open truly exciting doors for thinking about biology, a theme that runs throughout this text.' SIAM Review