Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

Stankovski, Tomislav; Duggento, Andrea; McClintock, Peter V. E.; Stefanovska, Aneta

doi:10.1103/physrevlett.109.024101

Cited by 143 publications

(244 citation statements)

References 40 publications

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“…It has gained increased interest due to extensive application of ideas from nonlinear dynamics and information theory to medical problems, for example, to the use of heart rate variability (HRV) as an indicator of autonomic activity. As a result, many aspects of cardiorespiratory coordination, like the degree of locking and the directionality of interaction, have been investigated 26,28,29,[34][35][36][37][38][39][40] .…”

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confidence: 99%

In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Frühwirth²,

et al. 2013

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Recovering interaction of endogenous rhythms from observations is challenging, especially if a mathematical model explaining the behaviour of the system is unknown. The decisive information for successful reconstruction of the dynamics is the sensitivity of an oscillator to external influences, which is quantified by its phase response curve. Here we present a technique that allows the extraction of the phase response curve from a non-invasive observation of a system consisting of two interacting oscillators-in this case heartbeat and respiration-in its natural environment and under free-running conditions. We use this method to obtain the phase-coupling functions describing cardiorespiratory interactions and the phase response curve of 17 healthy humans. We show for the first time the phase at which the cardiac beat is susceptible to respiratory drive and extract the respiratory-related component of heart rate variability. This non-invasive method for the determination of phase response curves of coupled oscillators may find application in many scientific disciplines.

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confidence: 99%

In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Frühwirth²,

et al. 2013

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“…When treated in an inverse approach such systems are usually considered as stochastic. In an attempt to cope with the problem, several methods for the inverse approach were introduced, including wavelet-based decomposition [14], bispectral analysis [15], harmonic detection [16] and phase coherence [17], and Bayesian-based inference [18] methods.…”

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confidence: 99%

Chronotaxic Systems: A New Class of Self-Sustained Nonautonomous Oscillators

2013

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Nonautonomous oscillatory systems with stable amplitudes and time-varying frequencies have often been treated as stochastic, inappropriately. We therefore formulate them as a new class and discuss how they generate complex behavior. We show how to extract the underlying dynamics, and we demonstrate that it is simple and deterministic, thus paving the way for a diversity of new systems to be recognized as deterministic. They include complex and nonautonomous oscillatory systems in nature, both individually and in ensembles and networks. DOI: 10.1103/PhysRevLett.111.024101 PACS numbers: 05.45.Xt, 05.65.+b, 05.90.+m, 89.75.Fb Dynamical systems are generally seen as being either deterministic or stochastic. The advent of dynamical chaos several decades ago attracted much attention and illustrated that even complex dynamics can be deterministic. Dynamical systems can also be classified as autonomous (self-contained) or nonautonomous (subject to external influences). In reality, nonautonomous systems are the commoner, but they are far harder to treat. Until now they were mostly treated as stochastic or, alternatively, attempts were made to reformulate them as autonomous. Neither approach captures the characteristic properties of these systems.In this Letter we propose a new class of nonautonomous systems and name them chronotaxic to characterize oscillatory systems with time-varying, but stable, amplitudes and frequencies. Nonautonomous oscillatory systems appear in various fields of research including neuroscience [1,2], cardiovascular dynamics [3], climate [4,5] and evolutionary science [6], as well as in complex systems and networks [7][8][9]. Although we are witnessing a rapid development of the theory of nonautonomous [10,11] and random dynamical systems [12,13], nonautonomous oscillatory systems with stable but time-varying characteristic frequencies have to date not been addressed. When treated in an inverse approach such systems are usually considered as stochastic. In an attempt to cope with the problem, several methods for the inverse approach were introduced, including wavelet-based decomposition [14] Common to all these systems is that they are oscillatory, have stable amplitudes, and frequencies that are resistant to external perturbations. The variety of systems with these characteristics suggests that their dynamics are generated from a universal basis. To date, the description of stable oscillatory dynamics has been based on the model of autonomous self-sustained limit cycle oscillators [23]. While this model provides stable amplitude dynamics, frequencies of oscillations within this model can be easily changed even by weakest external perturbations.The new class of nonautonomous oscillatory dynamical systems that we now propose account for such dynamics. The novelty of these systems is that not only are the amplitude dynamics stable but also the frequencies of the oscillations are time dependent and stable-i.e., their timedependent values cannot be easily altered by external perturbations. Their c...

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“…Many efficient methods for coupling detection have been designed [11,15,17,21,[36][37][38][39][40][41][42], and they are based around two main aspects. The first aspect is that the assessment of the strength of the interaction and its predominant direction can be used to establish if certain interactions exist at all.…”

Section: Interaction Analysis -Inverse Approachmentioning

confidence: 99%

“…These varying coupling functions can change in time the physical rules for the interactions, which can cause transitions of physical effects and phenomena, as the most important outcome of the interactions. For example, the time-varying cardiorespiratory coupling function was shown to induce transitions in and out of synchronization, and between different synchronization ratios [17]. Therefore, understanding the effects of the time-varying coupling functions on the interactions is of great interest, especially in understanding, detecting and interpreting the interactions of open (biological) systems.…”

Section: Introductionmentioning

confidence: 99%

“…Decomposition of a coupling function can also facilitate a description of the functional contributions from each separate subsystem within the coupling relationship. Different methods for coupling function detection have been applied widely in chemistry [10,11,[14][15][16], in cardiorespiratory physiology [12,13,17], in neuroscience [18][19][20], in mechanical interactions [21], in social sciences [22] and in secure communications [23]. The study of coupling function is a very active and expanding field of research [24].…”

Section: Introductionmentioning

confidence: 99%

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Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

Stankovski

2017

Phys. Rev. E

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Interactions in nature can be described by their coupling strength, direction of coupling and coupling function. The coupling strength and directionality are relatively well understood and studied, at least for two interacting systems, however there can be a complexity in the interactions uniquely dependent on the coupling functions. Such a special case is studied here -synchronization transition occurs only due to the time-variability of the coupling functions, while the net coupling strength is constant throughout the observation time. To motivate the investigation, an example is used to present an analysis of cross-frequency coupling functions between delta and alpha brainwaves extracted from the electroencephalography (EEG) recording of a healthy human subject in a freerunning resting state. The results indicate that time-varying coupling functions are a reality for biological interactions. A model of phase oscillators is used to demonstrate and detect the synchronization transition caused by the varying coupling functions, during an invariant coupling strength. The ability to detect this phenomenon is discussed with the method of dynamical Bayesian inference, which was able to infer the time-varying coupling functions. The form of the coupling function acts as an additional dimension for the interactions and it should be taken into account when detecting biological or other interactions from data.

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Inference of Time-Evolving Coupled Dynamical Systems in the Presence of Noise

Cited by 143 publications

References 40 publications

In vivo cardiac phase response curve elucidates human respiratory heart rate variability

In vivo cardiac phase response curve elucidates human respiratory heart rate variability

Chronotaxic Systems: A New Class of Self-Sustained Nonautonomous Oscillators

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

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