MATH 305 Lecture Notes - Lecture 1: Phase Portrait, Chaos Theory, Equilibrium Point
Document Summary
Plane autonomous systems are a type of system of differential equations that describe the behavior of an object in two-dimensional space over time. "autonomous" because they do not depend explicitly on time. Instead, the equations describe how the variables change over time as a function of their current values. In a plane autonomous system, the variables are typically the position and velocity of an object in two-dimensional space. One of the key advantages of plane autonomous systems is that they can be visualized using phase portraits. A phase portrait is a graphical representation of the behavior of the system in phase space, which is a space where each axis represents one of the variables in the system. The phase portrait can be used to visualize the trajectories that the system follows over time, as well as to analyze the stability and behavior of the system. Engineers and scientists often use plane autonomous systems to model and analyze physical systems.
