An investigation of nonlinear mathematical models of dynamics has led to the selection of characteristics that could be useful for distinguishing mathematically between the behaviors of (1) intelligent or living systems and (2) nonliving systems. As contemplated here, an intelligent or living system could range from a natural or artificial single-cell organism at one extreme to the whole of human society at the other extreme, whereas a nonliving system could be, for example, a collection of interacting particles or mechanisms. Among other findings, the investigation has revealed that living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions.

One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it was assumed, in this investigation, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental/motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection has traditionally been recognized as a basic element of intelligence.

In this investigation, the motor dynamics were represented by (1) a generator of stochastic processes representing the motor dynamics of a nonlinear one-dimensional random walk plus (2) a model of the corresponding evolution of the dynamics in probability space. Associated with the probabilistic model of the motor dynamics was a nonlinear version of the Fokker-Planck equation representing the flows of information in probability space: this model was taken to represent both the mental dynamics and a probabilistic self-image of the dynamic system. It was postulated that if the dynamic system "possesses" its self-image, then it can predict future expected values of its parameters and change the expectations if they are not consistent with what is observed.

It was then shown that a living system according to this model can predict the future in terms of probabilities, because of the smoothness of the evolution in probability space (such smoothness does not exist in physical space because of irregularities of a random walk). This ability to predict increases chances for survival and can be considered a basic component of intelligence. It was shown that the coupled motor/mental dynamics can simulate such lifelike phenomena as emerging self-organization, decision-making based on "common sense," predator/prey evolutionary games, and a collective brain. Both the mental and motor dynamics can be implemented by hardware (e.g., neural networks or cellular automata), thereby enabling artificially intelligent systems to exhibit such lifelike phenomena.

This work was done by Michail Zak of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at  under the Information Sciences category.


This Brief includes a Technical Support Package (TSP).
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Characteristics of Dynamics of Intelligent Systems

(reference NPO-21037) is currently available for download from the TSP library.

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