Subject: managing innovation using stock and flow diagram

Posted by Jeffrey S. Levin on 2/1/2009
In Reply To:managing innovation using stock and flow diagram Posted by George Richardson on 1/30/2009

Message:

When I ran the original equation from George Richardson in my spreadsheet I observed the following things:

Stable/periodic oscillation is observed when a=1.

Stable/nonperiodic oscillation is observed when a=2.

Some oscillation prior to rapid exponential decay is observed when a > 2.


1. When a=1.0, and as the Initial Condition X(0) increases > 0.20, it takes the system longer to achieve its oscillation limits between 0 and +1.

2. If a=2.0, the system "settles" into nonperiodic oscillations between limits of -1 and +1.

3. However, when a=2.0, AND when the Initial Condition X(0) = 0.5, the behavior of the system is completely stable over time. This is interesting because you get two different types of system behavior for the same value of "a" (i.e., nonperiodic oscillations and a stable flat line).

4. If a=2.1, the system exhibits unstable rapid exponential decay -- a=2.1 appears to be a "tipping point" here.

5. The system will accelerate into exponential decay more rapidly as "a" is increased further.

6. Overall, it appears that this system (i.e., the equation from Richardson) can exhibit widely varying types of behavior depending on rather small changes to the factor values and/or initial conditions.

Does anyone else note similar observations?

Best Regards,
Jeff Levin