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Unformatted text preview: x = a where a is also an arbitrary constant. 3 (3) The following discrete model is given to model population (2) x n +1 = 3 x 2 n x 2 n + 2 (a) Determine the nonnegative equilibria of the model (2). Determine the stabilities of the equilibria. (b) Suppose a fraction a is removed from the population in each generation so that the model becomes x n +1 = 3 x 2 n x 2 n + 2ax n . For what values of a is there a stable equilibrium only at x ∗ = 0? 4 (4) Given the population model with delay (3) N ′ ( t ) = rN ( tτ ) N ( tτ ) + AdN ( t ) where r, A, d are parameters. (a) Find the equilibria of model (3). (b) Find the characteristic equation of model (3). (c) Find conditions for stability of the equilibria. (d) Use computer algebra system to graph a representative solution of the model which stabilizes to sustained oscillations. Graph N as a function of t . 5...
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This note was uploaded on 03/20/2012 for the course MAP 4484 taught by Professor Martcheva,m during the Spring '08 term at University of Florida.
 Spring '08
 Martcheva,M

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