Detecting Periodic Unstable Points in Noisy Chaotic and Limit Cycle Attractors with Applications to Biology

Recently, biological preparations which are thought to be chaotic have been controlled using algorithms based on the detection and manipulation of periodic unstable points. The dynamics of these systems are, however, contaminated with noise; thus detection becomes a statistical process. Here we show that low dimensional chaos can be reliably detected with large noise contamination and distinguished from noisy limit cycles. We also examine a purely chaotic high dimensional system.