An attractor is a 'set', 'curve', or 'space' that a system irreversibly evolves to if left undisturbed. It is other-wise known as a 'limit set'. There are three types of attractors; point attractors, periodic attractors and strange attractors, all of which are discussed below.
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2 Phase space 3 The three types of attractors 4 Further reading 5 External link |
For instance, if you drop a book, it will land on the floor, and stop moving. This final state is the attractor of the system of "the book dropping". The book has now lost its potential energy, and is in a state of equilibrium. The type of attractor exhibited by this phenomena is known as a 'point attractor', because the limit set consists of a single point: position = constant, velocity = zero, acceleration = zero. Mathematically stated (see differential equations), we say:
The trajectory representation of a single-variable system is:
A strange attractor is a non-periodic attractor. This is the most common type of attractor. It is characterized by a set of coupled nonlinear partial differential equations. The first strange attractor discovered was the Lorenz attractor, discovered by the meteorologist Edward Lorenz, while simulating weather on a computer.
The Lorenz attractor is defined by a set of 3 coupled nonlinear differential equations:
These last two types of attractors are exhibited by what are called dissipative systems. Dissipative systems are systems not in thermodynamic equilibrium, but constantly "evolving towards" equilibrium. That is, they are characterized by a flow of entropy, and mutually, a flow of energy.