**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

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If the state space of a dynamical system is finite in extent, there will be a subset of the state space to which all trajectories are attracted as time passes, called the **attractor** of the dynamical system. For the simplest systems the attractor is a single point, which represents a **state of equilibrium** of the system. The physical interpretation is that for any initial state the system always approaches the state of equilibrium as time passes. For more complicated systems, the attractor can be a trajectory that is a **closed curve**, which represents a system performing regular **oscillations**. The physical interpretation is that for any initial state the system begins to perform regular oscillations as time passes. But in general nonlinear dynamical system of dimension three or more exhibit chaotic behaviour, and the attractor does not have a simple geometric description: the long-term behaviour of the system appears to be **unpredictable**, as with the double pendulum. For a chaotic system the attractor is called a **strange attractor**.

The most famous strange attractor is the **Lorenz attractor**, which is associated with a three-dimensional dynamical system, studied by Edward Lorenz in 1963, in connection with a problem in meteorology. See an image of the Lorenz attractor.

**Contact Info**

Department of Applied Mathematics

University of Waterloo

Waterloo, Ontario

Canada N2L 3G1

Phone: 519-888-4567, ext. 32700

Fax: 519-746-4319

PDF files require Adobe Acrobat Reader

University of Waterloo

University of Waterloo

43.471468

-80.544205

200 University Avenue West

Waterloo,
ON,
Canada
N2L 3G1

The University of Waterloo acknowledges that much of our work takes place on the traditional territory of the Neutral, Anishinaabeg and Haudenosaunee peoples. Our main campus is situated on the Haldimand Tract, the land granted to the Six Nations that includes six miles on each side of the Grand River. Our active work toward reconciliation takes place across our campuses through research, learning, teaching, and community building, and is co-ordinated within our Office of Indigenous Relations.