A new dynamical model of brainstorming: Linear, nonlinear, continuous (simultaneous) and impulsive (sequential) cases

Abstract

a b s t r a c tIn this paper, we extended the linear dynamical model of [Brown, V., Paulus, P. B. (1996). A simple dynamic model of social factors in group brainstorming. Small Group Research, 27, on two accounts. First, we modelled the sequential type brainstorming using impulsive differential equations by treating each category as an impulse and tested its validity in the two experiments that investigated and demonstrated the beneficial effects of sequential priming and memory in individual brainstorming. Finally, we considered the nonlinear case of brainstorming in writing or brainwriting where dyads exchanged their ideas in a written format and that eliminated negative factors occurring in oral brainstorming (e.g., evaluation apprehension, free-riding, production blocking) and enhanced the upward performance matching, and conducted the second experiment in order to test its validity in this paradigm with the effects of sequential priming and memory. Comparisons showed good agreement between results of experiments and those of the mathematical model.

Taking a broad perspective before brainstorming.

“…Furthermore, providing participants 10 categories led them to generate more ideas than providing them with only two categories in the sequential task, with time al lotted the same in both conditions. Coskun and Yilmaz (2009) also found that the participants in a sequential condition generated more ideas in a brainstorming task than did the participants in the nonsequential condition. Because the partici pants were cued with categories every 5 min, the sequential participants steadily generated ideas throughout the 30 min of the brainstorming task.…”

Dynamic Models for Ideas Number Prediction in Brainstorming

“…In their experimentations in [9], Coskun and Yilmaz noted that in the first half of the brainstorming session, the non-cognitive model fits better to the number of ideas recorded than the cognitive model, and conversely, the cognitive model was better in the second half of the session. Therefore, the use of the both models (non-cognitive and cognitive) and our both optimization models (Euler based and RungeKutta based) could be interesting for the prediction of ideas number.…”

“…The matching is estimated by the distance between productions of an individual and the average of others' productions. Following Coskun and Yilmaz [9], we add the constraint ‫‬ ሺ‫ݐ‬ሻ Ͳ to model the fact that ideas rate is always positive or null. A possible effect of this constraint is to break the linearity of the differential equations.…”

“…As Coskun and Yilmaz in [9], to be more realistic, some physical constraints have been added. These constraints state that the rate of generated ideas (݃ ሺ‫ݐ‬ሻ), the rate of ideas in memory ‫ݏ(‬ ሺ‫ݐ‬ሻ) and the rate of expressed ideas ‫(‬ ሺ‫ݐ‬ሻ) must be positive or null.…”

“…Coskun and Yilmaz in [9] improved the models proposed by Brown and Paulus by adding physical constraints (such as the rate of ideas is always positive) to make these models more realistic and complete. In addition, they modified them to deal with two situations: the sequential situation where the problem is decomposed into sub-problems and each sub-problem is presented one after other to the group (called sequential brainstorming), and the situation of brainwriting.…”