Attractories

An attractor is a set of mathematical or physical systems towards which a system tends to evolve, for a wide variety of starting conditions of the system. The dynamics of an attractor is the subset of the phase space of a dynamical system where the system evolves over time. Attractors are an important concept in the study of dynamical systems and are used in various fields such as physics, engineering, economics, and biology.

There are several types of attractors, including point attractors, periodic attractors, and strange attractors. A point attractor is a single point in the phase space towards which the system evolves. A periodic attractor is a set of points that the system cycles through over time. A strange attractor is a set of points with a fractal structure that the system evolves towards.

Attractors are often used to model and predict the behavior of complex systems. For example, in economics, attractors can be used to model the behavior of markets and predict economic trends. In physics, attractors can be used to model the behavior of physical systems such as the weather or the behavior of particles in a fluid.

Attractors are also used in the study of chaos theory, which is the study of complex and unpredictable behavior in dynamical systems. In chaos theory, attractors are used to model the behavior of systems that exhibit chaotic behavior, such as the Lorenz system or the logistic map.

In summary, attractors are an important concept in the study of dynamical systems and are used in various fields to model and predict the behavior of complex systems. There are several types of attractors, including point attractors, periodic attractors, and strange attractors, and they are used in the study of chaos theory and other fields.