Noise-sustained fluctuations in stochastic dynamics with a delay.
Delayed responses to external drivers are ubiquitous in environmental, social, and biological processes. Delays may induce oscillations, Hopf bifurcations, and instabilities in deterministic systems even in the absence of nonlinearities. Despite recent advances in the study of delayed stochastic differential equations, the interaction of random drivers with delays remains poorly understood. In particular, it is unclear whether noise-induced behaviors may emerge from these interactions. Here we show that noise may enhance and sustain transient periodic oscillations inherent to deterministic delayed systems. We investigate the conditions conducive to the emergence and disappearance of these dynamics in a linear system in the presence of both additive and multiplicative noise.
Department of Environmental Sciences, University of Virginia, 291 McCormick Road, Charlottesville, Virginia 22904-4123, USA.
Paolo
P
D'Odorico
Francesco
F
Laio
Luca
L
Ridolfi
D000818:Animals; D003198:Computer Simulation; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D059629:Signal-To-Noise Ratio; D013269:Stochastic Processes; D013997:Time Factors