Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Stankovski, Tomislav; Pereira, Tiago; McClintock, Peter V. E.; Stefanovska, Aneta

doi:10.1098/rsta.2019.0039

Cited by 22 publications

(10 citation statements)

References 86 publications

(125 reference statements)

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“…The first of our findings (the increase of the strength of the respiratory–cardiac coupling in the SAS and BP) relates to the well-known phenomenon of RSA. The slower function (respiratory component) affects the quicker oscillator (HR; [ 15 ]). As the coupling strength increases, HR (during inspiration) acceleration is observed, and, when the coupling decreases (during exhaust), HR decelerates ( Figure 3 and Figure 8 ).…”

Section: Discussionmentioning

confidence: 99%

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Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

Gruszecka

Nuckowska

Waśkow

et al. 2021

Entropy

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The precise mechanisms connecting the cardiovascular system and the cerebrospinal fluid (CSF) are not well understood in detail. This paper investigates the couplings between the cardiac and respiratory components, as extracted from blood pressure (BP) signals and oscillations of the subarachnoid space width (SAS), collected during slow ventilation and ventilation against inspiration resistance. The experiment was performed on a group of 20 healthy volunteers (12 females and 8 males; BMI =22.1±3.2 kg/m2; age 25.3±7.9 years). We analysed the recorded signals with a wavelet transform. For the first time, a method based on dynamical Bayesian inference was used to detect the effective phase connectivity and the underlying coupling functions between the SAS and BP signals. There are several new findings. Slow breathing with or without resistance increases the strength of the coupling between the respiratory and cardiac components of both measured signals. We also observed increases in the strength of the coupling between the respiratory component of the BP and the cardiac component of the SAS and vice versa. Slow breathing synchronises the SAS oscillations, between the brain hemispheres. It also diminishes the similarity of the coupling between all analysed pairs of oscillators, while inspiratory resistance partially reverses this phenomenon. BP–SAS and SAS–BP interactions may reflect changes in the overall biomechanical characteristics of the brain.

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Section: Discussionmentioning

confidence: 99%

“…To tackle this problem, we analysed the phase dynamics of interacting oscillations. This allowed us to study the coupling functions[ 14 , 15 ]. Coupling functions describe how an interactions occur and are manifested.…”

Section: Introductionmentioning

confidence: 99%

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

Gruszecka

Nuckowska

Waśkow

et al. 2021

Entropy

Self Cite

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“…In several events involving iterations, such as physics, biology and chemistry phenomena and related knowledge, iteration events are manifestations of repetition in the order or disorder of elements that constitute an iteration [30,31]. Although the cause of iterations as well as their behavior are key topics as the coupling functions [32] in the search for iterated events. An important aspect raised in this research reflects on the discretization of iterated events in terms of knowing how they behave and how to reproduce the same event under new experimental conditions.…”

Section: Discussionmentioning

confidence: 99%

False Asymptotic Instability Behavior at Iterated Functions with Lyapunov Stability in Nonlinear Time Series

Telles¹

2020

Advances in Intelligent Systems and Computing

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Empirically defining some constant probabilistic orbits of 𝑓(𝑥) and 𝑔(𝑥) iterated high-order functions, the stability of these functions in possible entangled interaction dynamics of the environment through its orbit's connectivity (open sets) provides the formation of an exponential dynamic fixed point 𝑏 = 𝑆 𝑛+1 as a metric space (topological property) between both iterated functions for short time lengths. However, the presence of a dynamic fixed point 𝑓(𝑔(𝑥)) 𝑥+1 can identify a convergence at iterations for larger time lengths of 𝑏 (asymptotic stability in Lyapunov sense). Qualitative (QDE) results show that the average distance between the discontinuous function 𝑔(𝑥) to the fixed point of the continuous function 𝑓(𝑥) (for all possible solutions), might express fluctuations of 𝑔(𝑥) on time lengths (instability effect). This feature can reveal the false empirical asymptotic instability behavior between the given domains f and g due to time lengths observation and empirical constraints within a well-defined Lyapunov stability.

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“…Although VSG controls and VOCs are successful in smallscale and autonomous electric systems, like smart grids, their applicability in bulk power systems is still under discussion. One of the difficulties lies in the fundamental and scientific problem of how thousands of self-organized oscillators behave when they are coupled in circuits and what consequences this will bring (Stankovski et al, 2019). This is an open question in the field of coupled oscillators and, although it is not the topic of this paper, the behavioral characterization and understanding of the diverse non-linear oscillators existing in various types of VSCs seems to be crucial to answering this question.…”

Section: Introductionmentioning

confidence: 95%

Synchronizing Stability Analysis and Region of Attraction Estimation of Grid-Feeding VSCs Using Sum-of-Squares Programming

Zhang

Molinas

et al. 2020

Front. Energy Res.

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Grid-synchronizing Stability (GSS) is an emerging issue related to grid-feeding voltage-source converters (VSCs). Its occurrence is primarily related to the non-linear dynamics of a type of vastly applied synchronization unit-Phase-locked Loops (PLL). Dynamic characterization and modeling for the GSS analysis can be achieved using a simplified system model, which is a second-order and autonomous non-linear equation, but with the presence of an indefinite damping term. As revealed and demonstrated in this work, this indefinite damping effect can result in an inaccurate Region-of-Attraction (ROA) estimation of the traditional Equal Area Principle (EAP)-based method. To overcome this issue and achieve a valid ROA estimation, this paper adopts the sum-of-squares (SOS) programming technique, which is a numeric optimization method with SOS relaxations. The development and implementation of the SOS program for ROA estimation are presented. Numerical case studies and time-domain verifications demonstrate that this method is valid for GSS analysis, and an almost precise estimation is achieved in the first quadrant. This evidence makes the SOS method a promising tool for GSS analysis because the GSS problem is most concerned with the stability within the first swing cycle, i.e., in the first quadrant.

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Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

Cited by 22 publications

References 86 publications

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

Coupling between Blood Pressure and Subarachnoid Space Width Oscillations during Slow Breathing

False Asymptotic Instability Behavior at Iterated Functions with Lyapunov Stability in Nonlinear Time Series

Synchronizing Stability Analysis and Region of Attraction Estimation of Grid-Feeding VSCs Using Sum-of-Squares Programming

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