Uncertainty Principle for Control of Ensembles of Oscillators Driven by Common Noise

We discuss control techniques for noisy self-sustained oscillators with a focus on reliability, stability of the response to noisy driving, and oscillation coherence understood in the sense of constancy of oscillation frequency. For any kind of linear feedback control--single and multiple delay feedback, linear frequency filter, etc.--the phase diffusion constant, quantifying coherence, and the Lyapunov exponent, quantifying reliability, can be efficiently controlled but their ratio remains constant. Thus, an "uncertainty principle" can be formulated: the loss of reliability occurs when coherence is enhanced and, vice versa, coherence is weakened when reliability is enhanced. Treatment of this principle for ensembles of oscillators synchronized by common noise or global coupling reveals a substantial difference between the cases of slightly non-identical oscillators and identical ones with intrinsic noise.Comment: 10 pages, 5 figure

Noise Can Reduce Disorder in Chaotic Dynamics

We evoke the idea of representation of the chaotic attractor by the set of unstable periodic orbits and disclose a novel noise-induced ordering phenomenon. For long unstable periodic orbits forming the strange attractor the weights (or natural measure) is generally highly inhomogeneous over the set, either diminishing or enhancing the contribution of these orbits into system dynamics. We show analytically and numerically a weak noise to reduce this inhomogeneity and, additionally to obvious perturbing impact, make a regularizing influence on the chaotic dynamics. This universal effect is rooted into the nature of deterministic chaos.Comment: 11 pages, 5 figure

Effective phase description of noise-perturbed and noise-induced oscillations

An effective description of a general class of stochastic phase oscillators is presented. For this, the effective phase velocity is defined either by invariant probability density or via first passage times. While the first approach exhibits correct frequency and distribution density, the second one yields proper phase resetting curves. Their discrepancy is most pronounced for noise-induced oscillations and is related to non-monotonicity of the phase fluctuations

Sensitivity of the global submarine hydrate inventory to scenarios of future climate change

The global submarine inventory of methane hydrate is thought to be considerable. The stability of marine hydrates is sensitive to changes in temperature and pressure and once destabilised, hydrates release methane into sediments and ocean and potentially into the atmosphere, creating a positive feedback with climate change. Here we present results from a multi-model study investigating how the methane hydrate inventory dynamically responds to different scenarios of future climate and sea level change. The results indicate that a warming-induced reduction is dominant even when assuming rather extreme rates of sea level rise (up to 20 mm yr−1) under moderate warming scenarios (RCP 4.5). Over the next century modelled hydrate dissociation is focussed in the top ∼100m of Arctic and Subarctic sediments beneath 30–50TgCH4yr−1), although subsequent oxidation in the water column could reduce peak atmospheric release rates to 0.75–1.4 Tg CH4 yr−1