# hw 1 - x = d Give the solution of the dynamical system with...

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Calculus for the Life Science I MAT1330A , MAT1330B, MAT1330E Assignment 1 Due date: Sept. 23 Instructor (circle one): Jing Li , Catalin Rada , Frithjof Lutscher DGD (circle one): 1 , 2 , 3 , 4 Student Name (printed): Student ID Number: Question 1 The size of a bird population on an island located close to the cost of Newfoundland depends on the local growth rate (birth minus death) and the migration between the island and New- foundland. A discrete dynamical system modelling this population is x n +1 = 0 . 85 x n + 75 , n = 0 , 1 , 2 , 3 , . . . , where x n is the size of the bird population on the island after n years. 0 . 85 is the local growth rate and 75 is the yearly increase due to migration. a ) If x 0 = 200, then x 1 = , x 2 = , x 3 = b ) Give the updating function f of the dynamical system. f ( x ) = c ) Find the equilibrium point x * of the dynamical system.

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Unformatted text preview: x * = d ) Give the solution of the dynamical system with x = 200. x n = e ) Draw the solution of the dynamical system with x = 200 (four points are enough). 2 f ) Draw the cobweb diagram of the dynamical system with x = 200 (four iterations are enough). g ) Determine the stability of the equilibrium point using the cobweb diagram. The equilibrium point is Question 2 The dynamical system x n +1 = αx n 1 + βx n , n = 0 , 1 , 2 , 3 ,... plays a role in the analysis of nonlinear models of gene and neural networks. α and β are positive parameters. Suppose that α = 2 and β = 1, a ) If x = 2 . 5, then x 1 = , x 2 = , x 3 = b ) Find the equilibrium points x * of the dynamical system. x * =...
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