Assign.#2 - stability(b Draw the updating function and use...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Prof. SAMINA BASHIR, University of Ottawa, MAT 1330, Fall 2008 Assignment 2, due November 5, 8:30am in class Student Name Student Number DGD 1 (Monday) DGD 2 (Tuesday) DGD 3 (Wednesday) Problem 1: [4 points] Consider the following nonlinear DTDS for a bird population with Allee effect: x t +1 = f ( x t ) = 3 x 2 t 1 + x 2 t . Analyze this DTDS, i.e., determine the biologically relevant fixed points and their sta- bility. Draw the updating function and use cobwebbing to illustrate and confirm your analytical results. Problem 2: [8 points] Consider the following nonlinear DTDS for a logistically growing population with harvesting: x t +1 = f ( x t ) = 2 x t (2 - x t ) - hx t , where 0 h 4 denotes the intensity of harvesting. (a) Analyze this DTDS, i.e., determine the biologically relevant fixed points and their stability. Summarize your results in the form of a little table (there should be three qualitatively different cases ): range of h fixed point(s)
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: stability (b) Draw the updating function and use cobwebbing for h = 2 to illustrate your analysis. (c) Find the value of the parameter h that guarantees the highest harvest. (d) Find the smallest value of the parameter h at which the population goes extinct. Problem 3: [4 points] Give the equation of the tangent line to the curve y = sin(sin( x )) at ( x,y ) = ( π, 0). Problem 4: [6 points] Use the first and second order derivatives to sketch the graph of f ( x ) = x + 4 x 2 . You have to find the critical points, inflexion points, intervals where the function is increasing, . .., and the vertical and horizontal asymptotes if any. Problem 5: [4 points] Find the derivative of the following function. (a) f ( x ) = sin( x 2 )-1 tan( x 2 ) , (b) f ( x ) = ln(sin( x 3 ) + 2) . Simplify your answers as much as possible. 1...
View Full Document

This note was uploaded on 01/25/2011 for the course MAT 1330 taught by Professor Dumitriscu during the Spring '08 term at University of Ottawa.

Ask a homework question - tutors are online