Self-feedback delay induces extreme events in the theoretical Brusselator system

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2025. Vol. 112. No. 1. Article 014202.

Manivelan S. V., S. Sabarathinam, Thamilmaran K., Manimehan I.

We present a study of the theoretical Brusselator model with time-delayed self-feedback, demonstrating its ability to induce extreme events when delays in reaction processes significantly influence subsequent dynamics, with and without diffusion. Stability analyses reveal the mechanisms driving this behavior with respect to the delay time. The occurrence of extreme events is validated using various numerical and statistical tools, including phase portraits, time series, probability distribution functions, return periods, and spatiotemporal evolution. A comprehensive two-parameter scan delineates the parameter regimes where the extreme events emerge, alongside the identification of transient chaos within specific regions of the parameter space. To confirm these numerical findings, we constructed an analog electronic circuit that emulates the model, providing experimental validation of the predicted dynamics.

Keywords: analysis of time series, Chaos, applied data analysis, Data analysis and modeling, Complex system

Publication based on the results of: Complex language and semantic models in artificial intelligence (2025)