Experimental datasets on synchronization in simplicial complexes.

Abstract

Some real-world phenomena and human-made problems have been modeled as networks where the objects form pairwise interactions. However, this is a limited approach when the existence of high-order interactions is inherent in a system, such as the brain, social networks and ecosystems. The way in which these high-order interactions affect the collective behavior of a complex system is still an open question. For this reason, it is necessary to analyze theoretically, numerically and experimentally the consequences of higher-order interactions in complex systems. Here, we provide experimental datasets of the dynamics of three nonlinear electronic oscillators, namely, Rössler oscillators, interacting into a simplicial complex whose connections rely on both linear (diffusive) and nonlinear (high-order) coupling. It is well-known that Rössler systems only achieve the synchronization when they are coupled by means of $x$ or $y$ variable. Considering this fact, we designed our experiment considering four scenarios. The first one, when both linear and nonlinear coupling functions are introduced through the $x$ variable. The second one, occurring when linear coupling is introduced through the $x$ variable and the nonlinear coupling through the $y$ variable. The third case happens when the linear coupling is introduced through the $y$ variable whereas nonlinear coupling goes through the $x$ variable. The last case, when both linear and nonlinear coupling are introduced through the $y$ variable. For each scenario, we acquired 10000 times series when both the linear and nonlinear coupling strengths were modified. Each time series contained 30000 temporal points. These datasets are useful to corroborate the conditions to reach the synchronized state varying the linear/non-linear coupling strengths and to test new metrics for better understanding the effects of higher-order interactions in complex networks.