Dynamical Systems

 

They're Everywhere

Valuable Sites to Visit:

The Dynamical Systems and Technology Project

Variation in Dynamic Systems

Fract-Ed

Complexity On-line

Real-life Examples

The Chaos We Call Weather

The Society for Chaos Theory in Psychology and the Life Sciences

Complexity International

Math Archives - Non-linear Dynamics

Biologic

Chaos Theory and Marxism

Ecosystems, Stock Markets, Orbits, Clouds, Turbulence.......

Dynamical systems are systems that are in constant flux. Examples include the stock market, ecosystems, the weather, the human body...The list is endless. Traditional mathematics based on Newtonian principles has only been able to understand and model these systems by taking them apart and looking at the individual pieces. We can use linear equations to model the pieces, however, this gives us an incomplete picture of the behavior of these systems. Eventually, we run up against the need to model these systems using non-linear equations, most of which are unsolvable. But many of the pioneers in chaos discovered that graphing these equations using feedback loops allowed them to look at pictures of these systems, and we are beginning to understand much more about them using these graphs. The following demonstrations and activities provide more information to understand dynamical systems.

Demonstrations:

• Dynamical Systems:Simulations and Visualization:animated simulations of dynamical systems, including oscillation. Provides projects and links to information on chaos and dynamical systems.
• The Dance of Chance:demonstrates the chaotic nature within nature, including applications in various areas of science.
• Click-n 4.0:a program for creating mathematical models of dynamical systems.

Activities:

• Predator-Prey Model: an interactive site which demonstrates the predator-prey relationship and models using non-linear equations.
• The Game of Life: another interactive site for exploring the Game of Life using the principles of Chaos.
• Population Growth :using the generalized logistic equation, the author of this site demonstrates population growth.
• Cyber Field Trip to the Complexity and Artificial Life Research Site: a complex site whose members contribute information and activities on the interdependence of science, psyche and humanities. Much to see here.