| Organodynamics | Grant Holland, Apr 25, 2014 |
| Slide: What am I trying to accomplish? | |
| To develop a dynamical systems theory that á
Models a certain class of dynamical
complex adaptive systems more faithfully, with respect to certain
properties, than do some widely
adopted
theories. á
Yet,
does
not exceed the bounds of tractability. For
now,
I intend the theory to support computer modeling. Strategies for analytical solutions may come later. | Which class of dynamical complex adaptive systems? Includes
living and lifelike systems. Which properties? Will
be defined by a specified list of systemic properties; but will attempt to capture ÒlifelikenessÓ. Which widely adopted theories? Specifically,
nonlinear dynamics and chaos. |
| In other words, organodynamics can be considered as a complementary alternative to nonlinear dynamics, operating
under altered conditions. How does organodynamics differ from nonlinear dynamics? In three principal ways: 1. State and trajectory are defined in terms of system organization, rather than attributes of individual components (i.e. vectors in a manifold). 2. System dynamics are stochastic. While nonlinear dynamics is strictly deterministic. 3. The mathematical foundations of organodynamics are probability theory, stochastic processes and information theory; rather than systems of nonlinear differential equations. | Hope
to show that this class of complex adaptive dynamical systems can be described, alone, by probability
theory and its offshoots. Challenge:
Must
show that the introduction of chance variation (stochasticism) need not degenerate into wildly chaotic behavior over time, yet still allow a certain Òfreedom to maneuverÓ. |
Notes: