Slide 10 of 25
Notes:
Dynamic systems are generally of the form shown in the first equation. S is the current state of the system at a point in time. The state is characterized by a (potentially a very high dimensional) vector, which changes (denoted by ? ). over time The pattern of the change is a function of the current state, S, a set of parameters, and random forces or noise.
The Rescorla-Wagner (or Bush-Mosteller) model is an example of a simple dynamic system in which the state is characterized by a one-dimensional vector that changes as a linear function of difference between the asymptote and the current state. The Rescorla-Wagner model describes the results of learning as a change in the state of the system rather than in the encoding of any kind of copy of the specific experience.
Nonlinear functions are the most interesting and have received the most attention in recent years, but linear functions also play a role in learning, memory, and development. Nonlinear functions interacting on a local basis can lead to the emergence of new relationships that cannot be produced with linear functions. This is what we mean by self-organizing.
Nonlinear dynamic systems are relevant to understanding learning and development because they show how small changes in input at crucial times can lead to radically different behaviors.
Adam Smith’s model of the self-organizing market is another example of a dynamic system.
