DifferentialSatirChangeMath

Applying NetworkFlowMath to the SatirChangeModel, for each value N of system effectiveness, the change in the effectivity of a system in an immediate future can be determined by the value of dN/dt:

Where the change in system effectiveness dN/dt is positive, the dynamics will cause the effectiveness to increase. In regions of the N axis where dN/dt is negative, the dynamics will cause the effectiveness to decrease.

The dashed arrows indicate the direction of change in the immediate future if the initial value of N falls within that region.

If the change function f(Ne) is 0 for some system effectiveness, the value of N is an equilibrium value.

Multiple domains of attraction can be used for investigating "jumps" in cultural issues. “Jumps” are often associated with a continuous change in some system parameter. This can mean that a continuous change in a system parameter can cause a discontinuous –sometimes large– change in the system.

A stable focus inside an unstable limit cycle

An unstable focus inside a stable limit cycle

A stable limit cycle with causality loops

An unstable limit cycle with dualism

In a region of the SatirChangeModel where the slope is positive,the slightest displacement will cause SystemEffectiveness to move away from the equilibrium, as is the case with the Foreign Element and Integration equilibria. These equilibria are locally unstable.

In a region where the slope of the change curve is negative, like between the beginning of the curve and Late Status Quo and between the top of the middle positive maximum and the Transforming Idea, a sufficiently small displacement can cause the system to move back to the respective equilibrium values, resp. Status Quo and Chaos. In such cases the equilibrium is called a locally stable equilibrium. SufficientlySmall is within the domain of attraction. The Virginia Satir model has multiple domains of attraction: N0 < N < Late Status Quo and N1 < N < Transforming idea.

-- NynkeEtkFokma, 2002