Question

Consider the discrete dynamical system given by the expression √1 + √1 + √1 + √1 + ⋯ where the " ⋯ " means the pattern continues forever. (A) Find a recurrence equation that models this pattern. (B) Instead of solving the recurrence equation, build a table of values from the recurrence equation through 10 iterations. (C) Find the nonnegative fixed point of this system and apply the Stability and Oscillation theorem to determine the system’s behavior around the fixed point.

Consider the discrete dynamical system given by the expression 1+ 1+ J1 + V1 + ... (A) Find a recurrence equation that models this pattern. (B) Instead of solving the recurrence equation, build a table of values from the recurrence equation through 10 iterations. (C) Find the nonnegative fixed point of this system and apply the Stability and Oscillation theorem to determine the system's behavior around the fixed point.

Answer 1

a) anni= Vitan geCussence relation. 16) Let ao o than 10 iteracion a = 10 a=52, az = Viti, au= Vit Vitre, as= Sitsit THE a6 = VIAJASTATTEL, az= VHSH SHTATAS ag= Jou jít si * $TASTEST PESA ag = Jot Sie 17+ A TP S + S 210 = VIA SA STA SI ASTASHA + SASHS+52 Itsit T+5+5H +5 c) fixed point when anti= an an = ditan anu - ltan an -an-1=0 an = 1tr5 take any o 2 80 Fixed point a = 1tJS For Stability f(a) = Vitan f'ca- kultan ť (HST) = 3 2 53+55 2 80 stable equilbium Point-