Dynamic Systems UMass Amherst Information 动力系统马萨诸塞大学阿默斯特分校的信息.ppt

Dynamic Systems Agenda Dynamic systems Bit of history for cognition. Dynamic systems vocabulary. Bifurcations catastrophes. Chaos. Haken, Kelso, Bunz, 1985 From Symbols to Dynamics Computational view of mind Symbolic atoms. Serial processing. Syntactic manipulation as in logic or language. Worry about syntax, not semantics. Connectionism Distributed representations. Parallel processing. Good generalization. Graceful degradation. Recurrent nets incorporate temporal dynamics. From Symbols to Dynamics Is flight best understood by Flapping or Dynamics of airfoils, airflow, mass, etc? Is cognition best understood by Symbolic and logical reasoning or Some underlying system of temporal dynamics? Dynamical Cognitive Hypothesis The cognitive system is not a discrete sequential manipulator of static representational structures; rather, it is a structure of mutually and simultaneously influencing change. Dynamical Cognitive Hypothesis Cognitive processes do not take place in the arbitrary, discrete time of computer steps; rather, they unfold in the real time of ongoing change in the environment, the body, and the nervous system. Dynamical Cognitive Hypothesis The dynamical approach at its core is the application of the mathematical tools of dynamics to the study of cognition. Natural cognitive systems are dynamical systems, and are best understood from the perspective of dynamics. Basic Concepts System - a set of interacting factors (called state variables) whose values change over time. Learning, perception, maturity, sensation, communication, feeding, attitude, motion, etc. State - vector of values, one for each variable of the system at a given moment. Maturity Example Basic Concepts State Space - all possible states of the system. State Variables - the variables used to define the state space. Trajectory - a curve connecting temporally successive points in a state space. Maturity Example Basic Concepts Phase Portrait - a state space filled with trajectories of a given