Abstract
Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist’s toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available.
Highlights
Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature
A system is chaotic if it is bounded, and if it is deterministic, and if tiny perturbations to the system get exponentially amplified (Glossary (Supplementary Information), Supplementary Figs. 1, 2)
If all that is available are measurements of how a real, non-simulated system evolves over time—for e.g., how a neuron’s membrane potential changes over time, or how the brightness of a star changes over time—. How can it be determined if those observations come from a chaotic system? Or if they are just noise? Or if the system is periodic (Glossary, Supplementary Figs. 1, 2), meaning that, like a clock, small perturbations do not appreciably influence its dynamics?
Summary
Exponential sensitivity to small perturbations, appears everywhere in nature. The meteorologist Edward Lorenz famously described this phenomenon as the butterfly effect: in a chaotic system, something as small as the flapping of a butterfly’s wings can cause an effect as big as a tornado This conceptually simple phenomenon—i.e., extreme sensitivity to small perturbations—is thought to appear everywhere in nature, from cosmic inflation[1], to the orbit of Hyperion[2], to the Belousov–Zhabotinskii chemical reaction[3], to the electrodynamics of the stimulated squid giant axon[4]. These are only a few examples of the many places in nature where chaos has been found. How can it be determined if those observations come from a chaotic system? Or if they are just noise? Or if the system is periodic (Glossary, Supplementary Figs. 1, 2), meaning that, like a clock, small perturbations do not appreciably influence its dynamics?
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