Organodynamics

Grant Holland, Apr 25, 2014

Slide: Constraints on Uncertainty Range

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Implementing the other four OCS organizing principles:

 

Dualistic aspect of the behavioral constraints on dynamical complex adaptive systems:

 

á      CanÕt be too chaotic (uncertain): The change-of-organization of an ODSP over time can be constrained so that it cannot be wildly chaotic indefinitely.

á      CanÕt be too predictable (certain):  An ODSP can change its organization enough to be able to adapt.

 

Limited Stationary Processes

 

An organic complex system entity canÕt sustain too much unstability or too much stability, but will exhibit some intermediate level of stability over some finite time span.

 

In organodynamics, organic complex systems can be represented by stationary distributions (ODSPs) that persist for some finite time span. We call these limited stationary distributions.

 

Autocoorganization

 

Can be understood as the ability of organodynamics to ÒregulateÒ the behavior of an ODSP so that it eventually stays within the above two bounds, and occasionally develops limited stationary distributions.

 

How to measure degree of ÒchaosÓ:

 

Chaos (def): ÒWhere chance reigns supreme

 

As differentiated from the definition of chaos in nonlinear dynamics (NLD) Ð which disallows chance, because NLD is strictly deterministic.

 

In organodynamics, the measure of the degree of ÒchaosÓ is the measure of the degree of uncertainty: statistical entropy and the entropic functionals.

 

 

Thus, information theory and its entropic functionals can characterize the degree of uncertain (chaotic) behavior of an ODSP that represents a complex dynamical system.

 

The dynamics of these systems must involve some constraints on the behavior or these systems.

 

 

Our Strategy

 

We must show that there are conditions under which the stochastic dynamics of ODSPs are constrained so that they tend toward some range that lies between too much and too little uncertainty Ð as measured by entropic functionals.

 

Notes: