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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.
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.
Language:
English
Keywords: analysis of time series Chaosapplied data analysisData analysis and modelingComplex system
Publication based on the results of:
Богатырев А. Б., Математический сборник 2023 Т. 214 № 3 С. 106–119
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Богатырев А. Б., Gendron Q., Успехи математических наук 2023 Т. 78 № 1 С. 209–210
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Богатырев А. Б., Transactions of the Moscow Mathematical Society 2024 Vol. 85 No. 2 P. 323–337
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Gendron Q., Compositio Mathematica 2025 Vol. 161 No. 7 P. 1483–1511
A Pell–Abel equation is a functional equation of the form P^2-DQ^2=1 , with a given polynomial D free of squares and unknown polynomials P and Q. We show that the space of Pell–Abel equations with the degrees of D and of the primitive solution P fixed is a complex manifold. We describe its connected components ...
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Beck M. E., Seidov S., Mukhin S., Physical Review A: Atomic, Molecular, and Optical physics 2026
Quantum dissipation is studied in the superradiant phase of the extended Dicke model. It is demonstrated analytically by quantum mechanical derivation of the Lindblad equation for the Dicke model in the superradiant state coupled to Caldeira-Leggett thermal bath that the effective viscosity appearing in the semiclassical equations of motion of polaritonic condensate survives in the zero-temperature limit ...
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Seidov S., Pugach N., Physical Review B: Condensed Matter and Materials Physics 2026
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Cham: Springer, 2026.
This book constitutes the proceedings of the 10th International Workshop Empowering Novel Geometric Algebra for Graphics and Engineering, ENGAGE 2025, held in conjunction with Computer Graphics International conference, CGI 2025, in Hong Kong, China, on July 14, 2025.
The 14 full papers included in this volume were carefully reviewed and selected from 16 submissions. The papers ...
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Marshakov A., Yung A, Ievlev E. et al., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 114 Article 046006
We continue the study of non-Abelian vortex string in 4D N =2 supersymmetric QCD (SQCD) as
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Ratnikov F., European Physical Journal: Special Topics 2026 P. 1–10
EEG recordings are often affected by the loss or corruption of individual channels due to electrode detachment, poor scalp contact, or external interference. Such channels must be accurately reconstructed before further analysis. In this study, we investigate Next-Generation Reservoir Computing (NG-RC) as a data-driven approach for reconstructing corrupted EEG channels and compare its performance with ...
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Ratnikov F., Bocharnikov V., Journal of High Energy Physics 2026 Vol. 2026 P. 1–21
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Budkov Y., Kalikin N., Journal of Chemical Physics 2026 Vol. 165 Article 064506
A self-consistent statistical-mechanical theory of the Hall effect in electrolyte solutions is developed by extending the self-consistent Debye–Hückel–Onsager (SCDHO) framework to crossed electric and magnetic fields. The theory incorporates non-local ionic charge distributions via Slater-type form factors, regularizing the Coulomb interaction at short range, and accounts for dielectric friction through ion-specific coefficients, employing experimental values ...
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Speranski S. O., Математические заметки 2026 Т. 120 № 3 С. 470–483
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Minets M., Krasnozhenov G., Trofimova E. et al., PeerJ Computer Science 2026 Vol. 12 Article e4063
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Мизинов П. В., Journal of Computer Virology and Hacking Techniques 2023 No. 20 P. 383–396
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Ali S., Bocharnikov V., Ratnikov F. et al., Sensors 2026 Vol. 26 No. 16 Article 5024
Large distributed sensor arrays require repeated recalibration as radiation damage, material aging, gain variation, and readout drift alter channel responses. We studied a high-granularity calorimeter as a large sensor array and addressed unsupervised recalibration from two unpaired datasets: a nominal reference response and an aged response with attenuated cell-wise signals. Aging was modeled by a ...
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Tsydypova M., Современные проблемы дистанционного зондирования Земли из космоса 2026 Т. 23 № 3 С. 263–275
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Trubochkina N. K., М.: Издательство «Юрайт», 2026.
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Springer, 2026.
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Kim J., Lee H., Jeon H. et al., , in: CIKM '25: Proceedings of the 34rd ACM International Conference on Information and Knowledge Management.: ACM, 2025. P. 1344–1353.
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