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Consider the recursive relation x_(t+1)=c(4x_(t))/(1+x_(t)) where c>0 is an unknown constant. (a) Find all equilibrium points. Answer: x= and x= (b) For
Consider the recursive relation\
x_(t+1)=c(4x_(t))/(1+x_(t))
\ where
c>0
is an unknown constant.\ (a) Find all equilibrium points.\ Answer:
x=
\ and
x=
\ (b) For which values of
c
is the zero equilibrium stable and the other one unstable?\ Answer:
c
\ (c) For which values of
c
is the zero equilibrium unstable and the other one stable?\ Answer:
c
\ (d) Let us call
c^(**)
the critical value that distinguishes the two cases above. What is the\ value of
c^(**)
?\ Answer:
c^(**)=
\ (e) In the case of
c=c^(**)
, we cannot say anything about the stability since
|f^(')((\\\\bar{x} ))|=
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