Question

Consider the dynamical system $S_{t+1} = S_t(1 - S_t)/2$ for $t = 0, 1, 2, 3, \dots$ Part 1 Find the fixed points. in terms of the initial condition $q_0$, the parameter $a$, and the number $n$. Part 2 [1] If $S_0 = 0.01$, calculate $S_1, S_2, S_3$, and $S_4$. [2] If $S_0 = 0.01$, calculate $S_1, S_2, S_3$, and $S_4$. [3] Based on the above calculations, what can you infer about the stability of one of the fixed points? Part 3 [1] If $S_0 = 0.9$, calculate $S_1, S_2, S_3$, and $S_4$. [2] If $S_0 = 1.1$, calculate $S_1, S_2, S_3$, and $S_4$. [3] Based on the above calculations, what can you infer about the stability of one of the fixed points?

          Consider the dynamical system
$S_{t+1} = S_t(1 - S_t)/2$ for $t = 0, 1, 2, 3, \dots$

Part 1
Find the fixed points.
in terms of the initial condition $q_0$, the parameter $a$, and the number $n$.

Part 2
[1] If $S_0 = 0.01$, calculate $S_1, S_2, S_3$, and $S_4$.
[2] If $S_0 = 0.01$, calculate $S_1, S_2, S_3$, and $S_4$.
[3] Based on the above calculations, what can you infer about the stability of one of the fixed points?

Part 3
[1] If $S_0 = 0.9$, calculate $S_1, S_2, S_3$, and $S_4$.
[2] If $S_0 = 1.1$, calculate $S_1, S_2, S_3$, and $S_4$.
[3] Based on the above calculations, what can you infer about the stability of one of the fixed points?

Consider the dynamical system
St+1 = St(1 - St)/2 for t = 0, 1, 2, 3, …

Part 1
Find the fixed points.
in terms of the initial condition q0, the parameter a, and the number n.

Part 2
[1] If S0 = 0.01, calculate S1, S2, S3, and S4.
[2] If S0 = 0.01, calculate S1, S2, S3, and S4.
[3] Based on the above calculations, what can you infer about the stability of one of the fixed points?

Part 3
[1] If S0 = 0.9, calculate S1, S2, S3, and S4.
[2] If S0 = 1.1, calculate S1, S2, S3, and S4.
[3] Based on the above calculations, what can you infer about the stability of one of the fixed points?

Added by Jeffery T.

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