Organodynamics

Grant Holland, Apr 25, 2014

Slide: A new complex dynamical systems theory

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Dynamical systems theories, such as classical mechanics and nonlinear dynamics, focus on numerical properties of individual point particlesÉ

 

Such as the position and momentum,

 

Or other states described by points in topological vector spaces and manifolds.

 

The dynamics of these systems are generally differentiable and deterministic.

 

This approach has sponsored a highly successful and essential program that has dominated applied mathematics for the past three centuries.

 

But we are also now turning our attention to applications, such as the life sciences, wherein our attention has moved to these aspects:

 

á      Networks of interrelationships among individual elements dominate our interests.

 

á      Individual elements are understood as rich systems in their own right.

 

In these matters, system organization prevails.

 

For example, biologists are primarily concerned with proteins, nucleic acids, cells, organelles, tissues, organs, organisms and how these elements are interrelated into highly complex organizationsÉ

 

And how these organizations change over time, including, reproduction, growth, development, metabolism and evolution.

 

Chemistry can be understood as the dynamics of atomic and molecular reorganization.

 

 

Moreover, at every level of biological organization, chance variation and fluctuation (e.g. diffusion processes) bring various degrees of uncertainty that nevertheless usually self-regulate.

 

In this presentation, I put forth a new complex dynamical systems theory, currently in development, which emphasizes system organization as it changes over timeÉ

 

And that also makes an accounting for the stochastic nature of complex systems.

 

I call this new theory organodynamics.

 

Notes: