Consider an ecological system described by the finite difference equation. x_t+1=C(x_n)^2(2-x_n) for 0≤x_n≤2
where x_n is the population density in year n and C is a positive constant that we assume is equal to 25/16.
a) Determine the fixed points of this system
b) In a brief sentence or two describe the expected dynamics starting from initial values of x_o=1/3 and also x_o=1 in the limit as n → ∞. In particular, comment on the possibility that
the population may go to extinction or to chaotic dynamics in the limit n → ∞.
my solution for a) 0,8/5,2/5 b) for x_o=1/3 the graph is converge

Question

Consider an ecological system described by the finite difference equation. x_t+1=C(x_n)^2(2-x_n) for 0≤x_n≤2
where x_n is the population density in year n and C is a positive constant that we assume is equal to 25/16.
a) Determine the fixed points of this system
b) In a brief sentence or two describe the expected dynamics starting from initial values of x_o=1/3 and also x_o=1 in the limit as n → ∞. In particular, comment on the possibility that
the population may go to extinction or to chaotic dynamics in the limit  n → ∞.
my solution for a) 0,8/5,2/5 b) for x_o=1/3 the graph is converge

yuffanhza · Answer

i want to know if my answer is true or false

irishboy123 · Answer

The FP's look good :-)

and seems it converges on extinction for x_0 = 1/3

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