Mathematical Biology Seminar

Kevin Lin University of Arizona
Wednesday Feb. 13, 2007
3:05pm in LCB 215
Reliability of coupled oscillators

Abstract: This talk concerns the reliability of coupled oscillator networks in response to complex, fluctuating stimuli. Reliability means that repeated presentations of a stimulus elicit essentially identical responses regardless of the system's state at the onset of the input. This work is motivated by basic questions from neuroscience, where the reliability of a network is relevant to how information may be encoded and transmitted. I will show how the question of reliability can be precisely formulated in the framework of random dynamical systems theory, and review the well-known fact that single phase oscillators are reliable. I will then show that unreliability can occur even in a 2-oscillator system, and propose a geometric mechanism for the observed phenomena. The talk will conclude with some observations concerning larger networks, including a natural condition which precludes unreliability. No prior knowledge of random dynamical systems theory is assumed. This is joint work with Eric Shea-Brown and Lai-Sang Young.