Dynamical Systems and Differential Equations

About dynamical systems research

Dynamical systems are mathematical models of how things change with time.

The time evolution is deterministic in the sense that there is some law of motion, often a differential equation, that determines future states from the present state of the system. Inferring long-time behavior from the law of motion can be incredibly intricate. Simple laws can lead to overwhelming complexity of the temporal evolution, yet simple collective behavior can emerge in large complex systems.

Dynamical systems research develops and uses tools that describe, predict, and at times classify this temporal behavior, simple or complicated. 

Applications

In applications, dynamical systems tools and methods inform modeling in the sciences, they enhance our understanding of phenomena, and they guide decisions in engineering and industry. Specific applications related to research in the group include:

• Space mission design.
• Melting ice sheets and global warming.
• Desertification in arid climates.
• Predicting the rise and fall of political parties.
• Quantifying transitions to spatio-temporal turbulence.