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Language: 
Russian
Heading: 
Nonlinear Dynamics and Neuroscience
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003165
EDN: 
QISLWL

Application of phase dynamics modeling and recurrence methods to assess the characteristics of the relationship between physiological rhythms

Autors: 
Dick Olga Евгеньевна,
Abstract: 

The purpose of this work is to apply two methods of nonlinear dynamics to assess the characteristics of the relationship between time series extracted from physiological rhythms. The analyzed time series were respiratory rhythm fluctuations, arterial pressure variability curves, and variability of neuronal activity intervals in the medulla oblongata of rats before and during pain exposure.

Methods. To solve the problem of identifying the relationship and assessing the asymmetry and direction of the relationship, a method for modeling the phase dynamics of weakly coupled and weakly noisy systems and a method for calculating averaged conditional probabilities of recurrences of time series generated by interacting systems were used. As characteristics of the relationship between systems, estimates of the intensity of the influence of one system on another and estimates in the differences of the averaged conditional probabilities of recurrences
were used.

Results. To verify the robustness of the applied methods to noise, an analysis of a well-studied model of unidirectionally coupled Van der Pol oscillators was performed. The correct determination of the direction of coupling by both methods with weak noise and a decrease in the possibility of identifying the direction by the phase modeling method with increasing noise, and the preservation of the possibility of correctly determining the direction by the recurrence method were confirmed. For experimentally obtained and weakly noisy biological time series, an asymmetry of the coupling with a predominant influence of the respiratory rhythm on the variability of neuronal activity and arterial pressure, and the influence of arterial pressure variability on the neuronal activity
of the reticular formation of the medulla oblongata was found in most of the analyzed data.

Conclusion. The application of two methods for assessing the characteristics of the relationship between weakly noisy time series, both model and experimental, showed quite consistent results in the predominant influence of one system on the other.
 

Key words: 
phase dynamics
recurrence
physiological rhythms
Acknowledgments: 
The work was supported by the State funding allocated to the Pavlov Institute of Physiology Russian Academy of Sciences (No. 1021062411784-3-3.1.8).
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Received: 
26.10.2024
Accepted: 
31.01.2025
Available online: 
03.02.2025
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