Question 2355: A Short Exact Orbit of the Specified Logistic Increment Model

Original question and givens

Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=4/25, rate=1/1, capacity=9/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

• G001 — Use exactly the fixed discrete increment model next=x+r*x*(1−x/K), with K>0, 0≤r≤1 and 0≤x≤K, at fixed time steps. Reduce exact rational outputs and omit /1 for integers. This is neither another logistic-map convention nor a continuous logistic solution; a finite orbit proves no stability, convergence or empirical population fit. initial=4/25, rate=1/1, capacity=9/1, updates=0. Give (initial,rate,capacity,update count,orbit including initial). With zero updates retain just the initial value.

Definition and scope

Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.

• mko-discrete-logistic-growth

Step-by-step derivation

0≤r=1≤1; K=9>0; 0≤x=4/25≤K

T(x)=x+r·x·(1−x/K)

initial=4/25; steps=0

retain the initial state before updating

orbit=[4/25]

entries=1=steps+1

Reverse checks

• S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.
• S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.

Result

(4/25, 1, 9, 0, [4/25])

The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.

This question review and source binding

Review date: 2026-10-26

Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.