Title: The Existence and Properties of Spatiotemporal Chaos in a 2D Excitable Medium
Speaker: Henry Greenside
Speaker Info: Duke University
Brief Description:
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Abstract:
Excitable media such as heart tissue and chemical reaction- diffusion systems often have complex dynamical states involving many spirals or filaments that nucleate, interact, and annihilate over time. Such states raise challenging and interesting questions at the frontier of nonlinear dynamics such as how to characterize such states, are they chaotic, and are there universal features of the dynamics. I will discuss research by my group [*] that addresses some of these questions by numerical simulations of the Bar model, a model in which complex dynamics arises from repeated spiral instabilities caused by Doppler shifts. Our analysis shows that what seems to be chaotic behavior is actually long-lived transients whose average decay time grows exponentially with the system size. Although transient, the many-spiral states are well described as chaotic with a fractal dimension that grows extensively with the size of the system and whose value is related to the average density of spiral defects. Applications of these ideas to the analysis of surface voltage data on fibrillating hearts will be discussed. [*] "Size-dependent Transition to High-Dimensional Chaotic Dynamics in a Two-Dimensional Excitable Medium" by M. Strain and H. Greenside, Phys. Rev. Lett. 80(11):2307-2309 (1998).Date: Friday, February 8, 2002