Linear and Nonlinear System Analysis

Mathematics is critical for the analysis of perceptual and other brain processes because it re presents the most powerful tool humans have developed [Page 530]for understanding and predicting the behavior of complex systems and their changing responses over time. The study of change over time is known as dynamics. Linear systems represent the simplest form of mathematical description of perceptual phenomena, and their characteristics are quite well understood. Nonlinear systems are much more complex and only partially understood. Fortunately, however, the types of nonlinearity characterizing the brain have been intensively studied for almost 50 years, so a substantial degree of understanding has been achieved. Most exciting is the observation that nonlinear systems can generate strikingly complex forms of response capable of explaining brain function, so ...