Order from Disorder (from Order)
Dynamics is the study of things that change in time. Non-linear dynamics can give rise to chaos, where tiny fluctuations are magnified so that they become unpredictible in a short time, even though the dynamics are generated from deterministic equations. Despite this unpredictability, chaotic systems can synchronize in a variety of ways. I study the ways in which chaotic systems act together in time and how this might apply to specific systems, such as neurons in the brain.
Resources
My Publications
- Waddell J and Zochowski M. “Network reorganization driven by temporal interdependence of its elements.” Chaos 16, 023106: 2006.
- Waddell J and Zochowski M. “Intraburst versus interburst locking in networks of driven nonidentical oscillators.” Physical Review E 76: 2007
- Feldt S, Waddell J, Hetrick VL, Berke JD, and Zochowski M. “Functional clustering algorithm for the analysis of neural relationships.” Submitted to Physical Review Letters. 2008.
Other Sources
- Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering . Steven Strogatz. A very good mathematical introduction into dynamical systems. Level: Advanced undergraduate.
- Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life. Steven Strogatz. A great pop-sci book about synchronization, how it works, and all the myriad places where it can be found. Level: Anybody.
- Synchronization: A Universal Concept in Nonlinear Sciences . Arkady Pikovsky, Michael Rosemblum, and Jurgen Kurths. An excellent and approachable technical text about synchronization, particularly of nonlinear dynamical systems. Level: Advanced undergraduate, though a good reference for specialists.