Cognitive Model - Dynamical Systems

Dynamical Systems

In the traditional computational approach, representations are viewed as static structures of discrete symbols. Cognition takes place by transforming static symbol structures in discrete, sequential steps. Sensory information is transformed into symbolic inputs, which produce symbolic outputs that get transformed into motor outputs. The entire system operates in an ongoing cycle.

What is missing from this traditional view is that human cognition happens continuously and in real time. Breaking down the processes into discrete time steps may not fully capture this behavior. An alternative approach is to define a system with (1) a state of the system at any given time, (2) a behavior, defined as the change over time in overall state, and (3) a state set or state space, representing the totality of overall states the system could be in. The system is distinguished by the fact that all of these states belong together; that is, a change in any aspect of the system depends on other aspects of the system.

A typical dynamical model is formalized by several differential equations that describe how the system’s state changes over time. By doing so, the form of the space of possible trajectories and the internal and external forces that shape a specific trajectory that unfold over time, instead of the physical nature of the underlying mechanisms that manifest this dynamics, carry explanatory force. On this dynamical view, inputs alter the system’s intrinsic dynamics, rather than specifying an internal state that describes some external state of affairs.