Studies of the collective behavior of coupled dynamical agents continue to reveal a broad range of phenomena. Such behavior has been studied by using models such as the Kuramoto model, which can be related to dynamics of, for example, Josephson junctions, laser systems, power grids, and even sociology. In mechanical systems, synchronization is commonly analyzed in limit cycle oscillators, such as clocks or Van-der-Pol oscillators, where analogies with the Kuramoto model can be drawn. Here, the authors analyze a parametrically excited nonlinear Mathieu oscillator network and demonstrate that introducing random interventions can promote synchronous collective behavior. Specifically, in the uncoupled limit, the method of averaging is utilized to show that parametric excitation results in multiple stable periodic orbits. This phase space geometry remains largely intact under moderate coupling strengths and gives rise to a multitude of stable steady states, most of which, most of which correspond to asynchronous behavior. In addition, the emergence of chimera states, where synchronous and asynchronous behaviors coexist, is observed. When weak stochastic input is introduced, the asynchronous behavior is suppressed, and after an initial transient phase, a synchronous collective behavior is found to emerge. Thus, introducing noise (i.e., temporal disorder) to disordered dynamics is found to lead to order. This counterintuitive effect suggests applications in systems ranging from rotating machinery to Josephson junction arrays.
A Wed, study studied this question.