mockMidtermF10solutions

mockMidtermF10solutions - MATH314, Modeling Realizable...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MATH314, Modeling Realizable Phenomena Practice Midterm Solutions Gidon Eshel, Physics Department, Bard College Annandale-on-Hudson, NY 12504-5000, x-7232, geshel@bard.edu . Remember: succinct and to the point and very clearly printed, no cursive ever. (1) Explain clearly in a sentence the Principle of Parsimony. If the simulation (model output) resembles reality well, and if the model cannot be simplified it wins! (2) For the scalar linear model dx dt = x please (a) point out the state vector, It is the 1-vector (a scalar) x . (b) obtain the general solution and state what information you need for it to be com- plete, dx dt = x = dx x = dt. = Z x ( t ) x (0) dx x = Z x ( t ) x (0) d ln x = Z t dt ln x ( t )- ln x (0) ln x t- ln x o = ln x t x o = t = x t x o = e t = x t = e t x o . So x o is the piece of information needed. (c) define, and characterize the condition(s) for, instability. If > (which means that e t > 1 for t > ), the model is unstable. (3) For the model df dt = f- 10 fg dg dt = 10 fg- g, please (a) Write down the state vector. (1) x = f g ! . 1 2 (b) Identify the coefficients and describe briefly their biological roles. is f s intrinsic growth rate. is g s intrinsic death rate. The interaction terms coefficients are given in terms of the above two. (c) Point out sources of nonlinearities. In f s evolution equation, it is the 2nd term,- fg/ 10 , and in g s evolution equa- tion, it is the 1st term, 10 fg/ 10 , because both contain mutually multiplied state variables....
View Full Document

This note was uploaded on 10/14/2010 for the course MATH 314 taught by Professor Mbelk during the Spring '10 term at Bard College.

Page1 / 5

mockMidtermF10solutions - MATH314, Modeling Realizable...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online