Researchers have developed an analytic model that shows how groups of people influence individual behavior. The model takes the computational information from a collective model (numerical solutions of thousands of equations) and uses it to exactly determine an individual’s behavior (reduced to one equation). The discovery was the product of ongoing research to model how an individual adapts to group behavior.

The work focused on constructing and interpreting the output of large-scale computer models of complex dynamic networks from which collective properties — such as swarming, collective intelligence, and decision-making — could be determined.

Psychologists and sociologists have intensely studied and debated how individuals’ values and attitudes change when they join an organization. The Army is interested in how this dynamic might be at play in terrorist organizations and conversely, how individuals become transformed during Army basic training. The more deeply leaders understand the process of learning and adaptation within a group setting, the more effective they will be in the training process.

The new kind of dynamic model of individual behavior quantitatively incorporates the dynamic behavior of the group. The analytic solution to this new kind of equation coincides with the predictions of the large-scale computer simulation of the group dynamics. The model consists of many interacting individuals who have a yes/no decision to make. When the individuals cannot make up their minds, they quickly switch back and forth between the two options, so they begin talking with their neighbors. Because of this information exchange, the numerical calculation using the computer model finds that people hold their opinions for a significantly longer time.

To model the group dynamics, a test used a new kind of equation, with a non-integer (fractional) rather than an integer derivative, to represent fluctuating opinions. In a group of 10,000 people, the influence of 9,999 people to disrupt an individual is condensed into a single parameter, which is the index for the fractional derivative. Whatever the behavior of the individual before joining the group, the change in behavior is dramatic after joining. The strength of the influence of the group on an individual’s behavior is compressed into a single number: the non-integer derivative.

Consequently, an individual's simple random behavior in making any other decision, when isolated, is replaced with behavior that might serve a more adaptive role in social networks. The behavior may be generic, but it remains to determine just how robust the behavior of the individual is relative to control signals that might be driving the network.

The research may suggest a new approach to artificial intelligence in which memory is incorporated into the dynamic structure of neural networks.

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