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JOURNALS // Izvestiya VUZ. Applied Nonlinear Dynamics // Archive

Izvestiya VUZ. Applied Nonlinear Dynamics, 2025 Volume 33, Issue 6, Pages 873–897 (Mi ivp681)

NONLINEAR DYNAMICS AND NEUROSCIENCE

Nonlinear properties of the brain theta rhythm

A. Yu. Dolininaab, E. M. Suleymanovac, M. V. Kornilovab, M. V. Sysoevaa, I. V. Sysoevab

a Peter the Great St. Petersburg Polytechnic University
b Saratov State University
c Institute for Higher Nervous Activity and Neurophysiology RAS, Moscow

Abstract: The purpose of this study is to identify nonlinearity of local brain field potential signals during theta rhythm. Methods. The nonlinearity in the signal is manifested in the synchronous behavior of the fundamental frequency and its higher harmonics; to detect this, skeletons in different frequency ranges were used, the phase synchronization index was calculated and cross-spectral analysis was performed. Results. The fundamental frequency and the second harmonic in the spectrum during the theta rhythm were identified from multi-hour recordings in 14 animals. Based on the skeletons constructed from these recordings, frequency synchronization between the fundamental frequency and the second harmonic in the ratio of 2:1 was diagnosed at intervals of up to 10 s in both symmetrical channels. Phase synchronization was also diagnosed in a number of recordings, but at shorter intervals (about 2–4 s). Conclusion. The study proved that the spectral component observed at the theta-rhythm in healthy laboratory animals in the signals of local brain field potentials at the range containing twice fundamental frequency of the rhythm is indeed the second harmonic of the fundamental frequency. Thus, the theta rhythm is often a significantly nonlinear signal.  

Keywords: time-frequency analysis, skeletons, frequency dynamics, theta rhythm.

UDC: 530.182

Received: 01.06.2025
Revised: 28.11.2025
Accepted: 08.07.2025

DOI: 10.18500/0869-6632-003188



© Steklov Math. Inst. of RAS, 2026