Biocomplexity - Stochastic Dynamical Dystems

The views expressed herein are the personal views of the author and do not reflect the views of NSF or the US Government. Summary Existing methods of complexity research are capable of describing certain specifics of biosystems over a given narrow range of parameters but often they cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes abrupt state transitions. Chaos tools have the potential of reaching to the essential driving mechanisms that organize matter into living substances. Our basic thesis is that while established chaos tools are useful in describing complexity in physical systems, they lack the power of grasping the essence of the complexity of life. This thesis is illustrated by sensory perception of vertebrates and the operation of the vertebrate brain. The study of complexity, at the level of biological systems, cannot be completed by the analytical tools that have been developed for non-living systems. We propose a new approach to chaos research that has the potential of characterizing biological complexity. Our study is biologically motivated and solidly based in the biodynamics of higher brain function. Our biocomplexity model has the following features: 1) it is high-dimensional, but the dimensionality is not rigid, rather it changes dynamically; 2) it is not autonomous and continuously interacts with and communicates with individual environments that are selected by the model from the infinitely complex world; 3) as a result, it is adaptive and modifies its internal organization in response to environmental factors by changing them to meet its own goals; 4) it is a distributed object that evolves both in space and time toward goals that it is continually reshaping in the light of cumulative experience stored in memory; 5) it is driven and stabilized by noise of internal origin through self-organizing dynamics. The resulting theory of stochastic dynamical systems is a mathematical field at the interface of dynamical system theory and stochastic differential equations. This paper outlines several possible avenues to analyze these systems. Of special interest are input-induced and noise-generated, or spontaneous state-transitions and related stability issues. The development of the theory of chaos in the past two decades has suggested a resolution of the discrepancy between mesoscopic (Freeman, 2000a) global order and aperiodic seemingly random activity at microscopic levels. In particular, models of deterministic chaos have been proposed, such as twist-flip maps and the Lorenz, Rössler, and Chua attractors, which are …