Entrainment Maps

Diekman, Casey O.; Bose, Amitabha

doi:10.1177/0748730416662965

Cited by 28 publications

(2 citation statements)

References 56 publications

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“…For instance, Kronauer (1999) developed limit cycle models to simulate the oscillatory nature of circadian rhythms [9–11]. Researchers have also utilized Poincare map methods to analyze these non-linear differential equation models, as demonstrated by Diekman and Bose (2016) in their construction of entrainment maps for various circadian models [12–15]. However, challenges remain in developing entrainment maps for arbitrary circadian systems [16].…”

Section: Introductionmentioning

confidence: 99%

Obscured Complexity: How External Cycles Simplify the Dynamics of the Endogenous Circadian Oscillator–take the time series of body temperature records as an example

Lin

2024

Preprint

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Background: Understanding circadian rhythms is crucial in various fields of biological research, as they play a fundamental role in the regulation of diverse biological processes, ranging from gene expression to physiological functions. Objective: This study aims to explore the complexity of circadian rhythm signals from a biological system. Without the permission of using experimental data, the mathematical model is utilized to simulate the intricate dynamics of the body temperature's circadian rhythms and investigate the impact of parameter variation on system behavior. Methods: The Duffing equation is constructed as the mathematical model for simulating circadian rhythms. A thorough discussion justifies the selection of the Duffing equation and establishes the proper parameter range, ensuring chaotic behavior in the system. Four different values of the driving force parameter gamma (0.32, 0.33, 0.34, and 0.35) are chosen to represent specific cases. Fourier analysis is employed to analyze the simulation data, revealing the frequency components present in the circadian rhythm signals. Entropy analysis along the Poincare sections is utilized to measure the system's behavior and aggregation of points. Results: The simulations exhibit distinct characteristics in terms of plain visualization, Fourier analysis, and entropy analysis along the Poincare sections. Under normal work sleep conditions (gamma=0.35), the system demonstrates specific resetting at particular times within a total period. In shift work (gamma=0.34) or long-term constant temperature (gamma=0.33) conditions, some of the resetting behavior diminishes, and the initial phase of the time series changes. When all external driving forces are eliminated (gamma=0.32), the system undergoes multiple resets within a given period. In such circumstances, the biological clock experiences more frequent resets to adapt to the independent operations of each subsystem. Without relying on external environmental cues for regulation, the biological clock relies on frequent resetting to maintain the stability and coordination of the entire system. These findings align with experimental data, although the lack of available experimental data prevents direct comparison in this paper. Conclusion: The simulations reveals variations in resetting behavior and the importance of frequent resets in the absence of external cues. The complexity arising from chaos allows the biological system to adapt and adjust to the intricacies of the external environment. The endogenous clock within the system, despite its inherent complexity, can dynamically optimize its entrainment with external cycles. However, the full complexity of the endogenous clock may be concealed within the system and not readily observable. These findings contribute to a better understanding of the complex dynamics of circadian rhythms. Future research should aim to validate these results through comparisons with experimental data.

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Section: Introductionmentioning

confidence: 99%

Obscured Complexity: How External Cycles Simplify the Dynamics of the Endogenous Circadian Oscillator–take the time series of body temperature records as an example

Lin

2024

Preprint

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“…In particular, systems defined on periodic phase spaces such as a circle or torus lead to discontinuous maps. Applications of such maps include cardiac dynamics 15 , circadian rhythms 16 , and sleep rhythms 17 , to name just a few.…”

Section: Introductionmentioning

confidence: 99%

Order-indeterminant event-based maps for learning a beat

Byrne¹,

Rinzel²,

Bose³

2020

Preprint

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The process by which humans synchronize to a musical beat is believed to occur through error-correction where an individual's estimates of the period and phase of the beat time are iteratively adjusted to align with an external stimuli. Mathematically, error-correction can be described using a two-dimensional map where convergence to a fixed point corresponds to synchronizing to the beat. In this paper, we show how a neural system, called a beat generator, learns to adapt its oscillatory behaviour through error-correction to synchronize to an external periodic signal. We construct a two-dimensional event-based map which iteratively adjusts an internal parameter of the beat generator to speed up or slow down its oscillatory behaviour to bring it into synchrony with the periodic stimulus. The map is novel in that the order of events defining the map are not a priori known. Instead, the type of error-correction adjustment made at each iterate of the map is determined by a sequence of expected events. The map possesses a rich repertoire of dynamics, including periodic solutions and chaotic orbits.

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Leveraging deep learning to control neural oscillators

Matchen

Moehlis

2021

Biol Cybern

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Entrainment Maps

Cited by 28 publications

References 56 publications

Obscured Complexity: How External Cycles Simplify the Dynamics of the Endogenous Circadian Oscillator–take the time series of body temperature records as an example

Obscured Complexity: How External Cycles Simplify the Dynamics of the Endogenous Circadian Oscillator–take the time series of body temperature records as an example

Order-indeterminant event-based maps for learning a beat

Leveraging deep learning to control neural oscillators

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