In many complex systems, self-organised criticality (SOC) provides a mechanism for the diversity of spatiotemporal scales that optimises the system’s response to omnipresent driving forces. Signatures of SOC are increasingly more evidenced in collective social behaviours. However, the spontaneous occurrence of critical states and their role in maintaining the system’s functional properties still need to be better understood; the reason can be related to the complexity of human interactions and the ubiquitous presence of cycles in social dynamics.

In this work, we shed new light on these issues based on a critical survey and the extensive data analysis of online social dynamics. Firstly, we highlight prominent features of human activity patterns, conditioned by circadian cycles and content-related interactions, that can affect the course of the dynamics from the elemental to the global scale.

We then analyse the prototypal time series of emotion-driven communications in the online social network MySpace to demonstrate the coexistence of SOC states with the modulated cyclical trends. Precisely, we determine avalanches of emotional comments exhibiting multifractal scaling, scale-invariant inter-avalanching behaviours and temporal correlations coexist with the cyclical trends of broad singularity spectra.

We demonstrate that similar multi-harmonic cycles occur in entirely different datasets, particularly the negative emotion-driven Diggs and the infection-rate data from recent epidemics.

Our results reveal the dynamical regime where the modulated cycles coexist with self-organised critical states; in contrast, in the cycles-dominated regime, exemplified by the infection time series, the nature of collective dynamics remains hidden behind the cycle modulation.

B. Tadic, M. Mitrovic Dankulov, R. Melnik, Evolving cycles and self-organised criticality in social dynamics, Chaos, Solitons & Fractals 171 (2023) 113459.