Simply speaking, a dynamical system is a system in which what will happen depends on what is happening now. Mathematically, a dynamic system is described by the differential equation:
dx/dt = f(x)
In discrete time, the equation is expressed as
xn+1 = f(xn)
In other words, the change in the state of the system is a function of the current state. Many phenomena can be modeled as dynamical systems, including the trajectory of a projectile through space, population growth, and recurrent neural networks.
Dynamical system is a useful approach to studing learning and cognition, which are based on interactions between sensory signals and motor actions. Sensory information triggers an action that causes further sensory information, which then elicits subsequent actions, constitutely an inseperable coupling between perception and behaviour. Therefore, modeling such phenomena as dynamical systems provides a good way of analyzing the sensory-motor interactions.
