1Demonstration 1 of 4
Two loops through one stock
How does an adoption path with both loops live depend on the strength of contact?
The rate is (innovation + imitation x adopters / market) x remaining market. Contact feeds growth while the remaining market feeds the brake, and the two together make the S-shape.
Adopters start at 1 in a market of 1000. innovation is the share of the remaining market that adopts from outside influence each step. imitation scales contact between adopters and the remaining market.
Predict first. If imitation rises from 0.15 to 0.45, does the peak adoption rate come earlier or later?
Choose an example
Constructed example: the chapter's model, with imitation and innovation values chosen for this reader.
Calculated values
- Adopters at step 10
- 340
- Adopters at step 20
- 938
- Adopters at step 40
- 1000
- Peak adoption rate
- 80.1 at step 12
First step: rate = (0.01 + 0.30 x 1 / 1000) x (1000 - 1) = 10.29, so adopters go from 1 to 11.29. Imitation feeds on adopters while the remaining market shrinks, so the rate peaks at 80.1 in step 12 and the stock approaches 1000.
Use the idea
Treat a growth curve as the output of two competing loops, and ask what state would make the second one bind.
Where the conclusion applies
One step is one period, the market is fixed at 1000 and nobody leaves. The conclusion fails if the market itself grows or adopters drop out.
Check your understanding: With imitation 0.30 and innovation 0.01, what is the first-step rate from 1 adopter?
Chapter 14 source: section "Adoption, with two loops". Demonstration C14-D01.
2Demonstration 2 of 4
Knockout at one state
At a given number of adopters, which loop changes the rate more when it is cut?
Cutting by freezing the variable the loop reads keeps the rest of the model intact. Early the remaining market is nearly full, so contact matters; later the adopters are many and the market is nearly spent, so saturation matters.
contact_from freezes the adopter pool the imitation term sees; potential_from freezes the remaining market. A loop's contribution is the absolute difference between the full rate and the rate with that loop cut.
Predict first. At 100 adopters with imitation 0.30, which loop contributes more?
Choose an example
Constructed example: the chapter's knockout calls at several states chosen for this reader.
Calculated values
- Rate, both loops live
- 80.0
- Rate, word of mouth cut
- 5.0
- Rate, saturation cut
- 160.0
- Contribution of word of mouth
- 75.0
- Contribution of saturation
- 80.0
- Leading loop
- saturation
Full rate = (0.01 + 0.30 x 500 / 1000) x (1000 - 500) = 80.0. Cutting word of mouth: 0.01 x 500 = 5.0, so it contributes 80.0 - 5.0 = 75.0. Cutting saturation: (0.01 + 0.15) x 1000 = 160.0, so it contributes 160.0 - 80.0 = 80.0. The larger contribution is saturation.
Use the idea
Ask which loop leads at the state the organization is in today, not which loop the structure contains.
Where the conclusion applies
One state at a time, a market of 1000 and innovation 0.01. A tie is reported as the reinforcing loop by the pack's rule, and with more loops the contributions would not add up.
Check your understanding: At 500 adopters with imitation 0.30, what is the contribution of word of mouth?
Chapter 14 source: section "Knockout". Demonstration C14-D02.
3Demonstration 3 of 4
The handover
At which step does dominance change hands, and does it change within the window?
Nothing about the model changes at the handover. The state moves from few adopters and a full market to many adopters and a nearly empty one, and the larger contribution passes from one loop to the other.
Each line is a loop's knockout contribution at every step of the run. The handover is the first step at which the leading loop differs from the step before.
Predict first. With imitation 0.30, does dominance change hands within 10 steps?
Choose an example
Constructed example: the chapter's run and handover_step, with imitation and window length varied for this reader.
Calculated values
- Handover
- step 12
- Leader at the start
- word of mouth
- Leader at the end
- saturation
- Peak of word of mouth
- 75.0
- Largest saturation
- 310.0
At step 11 the contributions are 72.8 (word of mouth) and 55.5 (saturation), so word of mouth leads. At step 12 they are 75.0 and 77.7, a difference of 77.7 - 75.0 = 2.7, so dominance passes to saturation. No parameter changed; only the state moved.
Use the idea
Write the window beside every dominance claim, and report 'no handover within the window' when that is the finding.
Where the conclusion applies
One scenario per state of the controls, innovation 0.01 and a market of 1000. A different start or input would move the handover, so one step number is not a property of the structure.
Check your understanding: With imitation 0.30 over 40 steps, at which step does dominance change hands?
Chapter 14 source: section "The handover". Demonstration C14-D03.
4Demonstration 4 of 4
The same intervention in two regimes
Does a referral incentive help as much after the handover as before it?
Before the handover the contact term is the live constraint, so raising imitation moves the rate. After it the remaining market is the constraint, and only more market moves the rate.
The baseline is imitation 0.30 in a market of 1000. A referral incentive raises imitation to 0.40. Expanding the market raises it to 1200. The bars are the adoption rate at the state the baseline run is in at the chosen step.
Predict first. At step 25, does the referral incentive or the market expansion change the adoption rate more?
Choose an example
Constructed example: the chapter's model with two interventions defined for this reader.
Calculated values
- Adopters at this step
- 63
- Leading loop
- word of mouth
- Baseline rate
- 27.1
- Rate with the intervention
- 33.0
- Change in the rate
- 5.9
Referral incentive (imitation 0.30 to 0.40) at step 4. With imitation 0.40: (0.01 + 0.40 x 63 / 1000) x (1000 - 63) = 33.0, against 27.1. The change is 33.0 - 27.1 = 5.9 new adopters per step at this state, while word of mouth leads. This compares rates at one state, not final outcomes.
Use the idea
Pair every intervention with the regime it acts in, and list what to do now separately from what to prepare.
Where the conclusion applies
A rate comparison at one state, with the baseline path held fixed. It says nothing about the cost of either intervention or the path the system would then follow.
Check your understanding: At step 4 the baseline has 63 adopters and a rate of 27.1; what rate does imitation 0.40 give?
Chapter 14 source: section "Dominance and leverage". Demonstration C14-D04.