Nonlinear Phenomena in Complex Systems, 2026, Vol.29, No.2, pp.195-204

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2026, Vol.29, No.2, pp.195-204

Feedback Effects on the Dynamics in a System of Binary-State Threshold Elements with Activity-Driven Interactions

N. E. Savitskaya and T. A. Fedorova

Feedback - understood as the mutual influence between the order parameter and the control parameter - is studied in a particular multi-element system. In the system considered, avalanche-like changes in a threshold characteristic of the elements, namely stresses, trigger switches in their binary states (opinions). The control parameter is the activity of the elements, which determines both the probability that an element is involved in an avalanche and the rules for updating its opinion. The order parameter is the system-averaged opinion. The feedback is introduced as a linear decrease of the activity with the square of the average opinion. Using analytical and numerical methods, we demonstrate that this form of feedback leads to the emergence of a new self-oscillatory stationary dynamical mode. It is shown that the feedback stabilizes the system's dynamics by reducing the fluctuations of the order parameter.

Key words: opinion dynamics, voter model, activity-driven networks, sandpile model

DOI: https://doi.org/10.5281/zenodo.21107422

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