Noise influenced response movement in coupled oscillator arrays with multi-stability

Abstract

In this work, the authors explore the influence of noise on the dynamics of coupled nonlinear oscillators. Numerical studies based on the Euler–Maruyama scheme and experimental studies with finite duration noise are undertaken to examine how the response can be moved from one response state to another by using noise addition to a harmonically forced system. In particular, jumps from a high amplitude state of each oscillator to a low amplitude state of each oscillator and the converse are demonstrated along with noise-influenced localizations. These events are found to occur in a region of multi-stability for the system, and the corresponding noise levels are reported. A method for recognizing how much noise is required to induce a change the system dynamics is developed by using the response basins of attraction. The findings of this work have implications for weakly coupled, nonlinear oscillator arrays and the manner in which noise can be used to influence energy localization and system dynamics in these systems.