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} ))|=

Consider the recursive relation xt+1=c1+xt4xt 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(x)=