Biocomplexity: adaptive behavior in complex stochastic dynamical systems

Existing methods of complexity research are capable of describing certain s pecifics of bio systems over a given narrow range of parameters but often t hey cannot account for the initial emergence of complex biological systems, their evolution, state changes and sometimes-abrupt state transitions. Cha os tools have the potential of reaching to the essential driving mechanisms that organize matter into living substances. Our basic thesis is that whil e established chaos tools are useful in describing complexity in physical s ystems, they lack the power of grasping the essence of the complexity of li fe. This thesis illustrates sensory perception of vertebrates and the opera tion of the vertebrate brain. The study of complexity, at the level of biol ogical systems, cannot be completed by the analytical tools, which have bee n developed for non-living systems. We propose a new approach to chaos rese arch that has the potential of characterizing biological complexity. Our st udy is biologically motivated and solidly based in the biodynamics of highe r brain function. Our biocomplexity model has the following features, (1) i t is high-dimensional, but the dimensionality is not rigid, rather it chang es dynamically; (2) it is not autonomous and continuously interacts and com municates 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 bot h in space and time towards goals that is continually re-shaping in the lig ht of cumulative experience stored in memory; (5) it is driven and stabiliz ed by noise of internal origin through self-organizing dynamics. The result ing theory of stochastic dynamical systems is a mathematical field at the i nterface of dynamical system theory and stochastic differential equations. This paper outlines several possible avenues to analyze these systems. Of s pecial interest are input-induced and noise-generated, or spontaneous state -transitions and related stability issues. (C) 2001 Elsevier Science Irelan d Ltd. All rights reserved.