State transitions in generic systems with asymmetric noise and communication delay

An important challenge in working with multi-agent systems is that in the presence of noise and communication delay, interactions between the individual agents can lead to unexpected complex system-wide behaviors. In this paper, we consider a generic model of two weakly coupled dynamical systems with communication delay, and show how noise on one system can drive large fluctuations in the other through the coupling interface. Moreover, the large fluctuation happens while the first system exhibits only small random oscillations. In the case of systems with multiple locally stable equilibria, we show how the expected time to transition between two equilibrium states scales as a function of the coupling and delay between the two systems. 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 are confirmed using Monte Carlo simulations.