Thomas W. Carr | Searcharxiv

arXiv2017

Asymmetric noise-induced large fluctuations in coupled systems

Networks of interacting, communicating subsystems are common in many fields, from ecology, biology, epidemiology to engineering and robotics. In the presence of noise and uncertainty, inter- actions between the individual components can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems, and show how noise in one part of the system is transmitted through the coupling interface. Working synergistically with the coupling, the noise on one system drives a large fluctuation in the other, even when there is no noise in the second system. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. Uncertainty effects are quantified by showing how characteristic time scales of noise induced switching scale as a function of the coupling between the two coupled parts of the experiment. In addition, our results show that the probability of switching in the noise-free system scales inversely as the square of reduced noise intensity amplitude, rendering the virtual probability of switching to be an extremely rare event. Our results showing the interplay between transmitted noise and coupling are also confirmed through simulations, which agree quite well with analytic theory.

cond-mat.stat-mech↗

arXiv2014

Noise Induced Switching and Extinction in Systems with Delay

We consider the rates of noise-induced switching between the stable states of dissipative dynamical systems with delay and also the rates of noise-induced extinction, where such systems model population dynamics. We study a class of systems where the evolution depends on the dynamical variables at a preceding time with a fixed time delay, which we call hard delay. For weak noise, the rates of inter-attractor switching and extinction are exponentially small. Finding these rates to logarithmic accuracy is reduced to variational problems. The solutions of the variational problems give the most probable paths followed in switching or extinction. We show that the equations for the most probable paths are acausal and formulate the appropriate boundary conditions. Explicit general results are obtained for small delay compared to the relaxation rate. We also develop a direct variational method to find the rates. We find that the analytical results agree well with the numerical simulations for both switching and extinction rates.

cond-mat.stat-mech↗