A dynamic systems model of cognitive and language growth.

In the first part of the article, a conceptual framework is sketched to define cognitive growth, including language growth, as a process of growth under limited resources. Important concepts are the process, level, and rate of growth; minimal structural growth level; carrying capacity and unutilized capacity for growth; and feedback delay. Second, a mathematical model of cognitive growth under limited resources is presented, with the conclusion that the most plausible model is a model of logistic growth with delayed feedback. Third, the model is transformed into a dynamic systems model based on the logistic growth equation. This model describes cognitive growth as a system of supportive and competitive interactions between growers. Models of normal logistic growth, U-shaped growth, bootstrap growth, and competitive growth are also presented. An overview is presented of forms of adaptation of resources (e.g., parental and tutorial assistance and support) to the growth characteristics of a cognitive or linguistic competence. Finally, the question of how the model can account for stages of growth is discussed.