Experimental demonstration of the ensemble approach for understanding the principles of drifting chaotic systems

Abstract Complex systems subjected to parameter drift require an ensemble approach in their investigation. In such cases, an individual trajectory is insufficient to capture the global changes in the system. In​ this paper we report the first experiment on low–dimensional chaotic mechanical systems subjected to considerable drift, resulting in six measured time series. Our set–up is based on three double pendula excited through the shaker, which allows to control and drift the excitation amplitude applied to the units. The equations of motion used for this system are shown to be consistent with the experiments: any single measurement is within the band of the ensemble simulation and traverses the band occasionally, after a sufficiently long time. The evaluation of the global dynamics can be understood with the concept of snapshot attractors , arising on the route from system initialization to a time–dependent chaotic steady state. The results presented in this paper experimentally confirm earlier simulation–only studies, expanding the concept of ensemble dynamics into more practical scenarios.