Synchronization Of Oscillators Research Articles

Accurate parameter identification method for coupled sub/super-synchronous oscillations for high penetration wind power systems

As the penetration of renewable energy increases to a large scale and power electronic devices become widespread, power systems are becoming prone to synchronous oscillations (SO). This event has a major impact on the stability of the power grid. The recent research has been mainly concentrated on identifying the parameters of sub-synchronous oscillation. Sub/Super synchronous oscillations (Sub/Sup-SO) simultaneously occur, increasing the difficulty in accurately identify the parameters of SO. This work presents a novel method for parameter identification that effectively handles the Sub/Sup-SO components by utilizing the Rife-Vincent window and discrete Fourier transform (DFT) simultaneously. To mitigate the impact of spectral leakage and the fence effect of DFT, we integrate the tri-spectral interpolation algorithm with the Rife–Vincent window. We use the instantaneous data of the phasor measurement unit (PMU) to identify Sub/Sup-SO-related parameters (Sub/Sup-SO damping ratio, frequency, amplitude and phase). First, the spectrum of the Sub/Sup-SO signals is analyzed after incorporating the Rife-Vincent window, and the characteristics of the Sub/Sup-SO signal are determined. Then, the signal spectrum is identified using a three-point interpolation algorithm, and the damping ratio, amplitude, frequency, and phase of the Sub/Sup-SO signals are obtained. In addition, we consider the identification accuracy of the algorithm under various complex conditions, such as the effect of Sub/Sup-SO parameter variations on parameter identification in the presence of a non-nominal frequency and noise. The proposed algorithm accurately identifies the parameters of multiple Sub/Sup-SO components and two Sub-SO components that are in close proximity. Testing with synthetic and real data demonstrates that the proposed algorithm outperforms existing methods in terms of identification accuracy, identification bandwidth, and adaptability.

Neural mechanisms of Chinese character recognition, updating, and maintenance in the N-back task

Using the N-back task, we investigated how memory load influences the neural activity of the Chinese character cognitive subprocess (recognition, updating, and maintenance) in Mainland Chinese speakers. Twenty-seven participants completed the Chinese character N-back paradigm while having their event-related potentials recorded. The study employed time and frequency domain analyses of EEG data. Results showed that accuracy decreased and response times increased with larger N values. For ERPs, N2pc and P300 amplitudes decreased and SW amplitude increased with larger N values. For time frequency analyses, the desynchronization of alpha oscillations decreased after stimulus onset, but the synchronization of alpha oscillations increased during the maintenance phase. The results suggest that greater memory load is related to a decrease in cognitive resources during updating and an increase in cognitive resources during information maintenance. The results of a behavioral-ERP data structural equation model analysis showed that the ERP indicators in the maintenance phase predicted behavioral performance.

Electroencephalography Spectral-power Volatility Predicts Problem-solving Outcomes.

Temporal variability is a fundamental property of brain processes and is functionally important to human cognition. This study examined how fluctuations in neural oscillatory activity are related to problem-solving performance as one example of how temporal variability affects high-level cognition. We used volatility to assess step-by-step fluctuations of EEG spectral power while individuals attempted to solve word-association puzzles. Inspired by recent results with hidden-state modeling, we tested the hypothesis that spectral-power volatility is directly associated with problem-solving outcomes. As predicted, volatility was lower during trials solved with insight compared with those solved analytically. Moreover, volatility during prestimulus preparation for problem-solving predicted solving outcomes, including solving success and solving time. These novel findings were replicated in a separate data set from an anagram-solving task, suggesting that less-rapid transitions between neural oscillatory synchronization and desynchronization predict better solving performance and are conducive to solving with insight for these types of problems. Thus, volatility can be a valuable index of cognition-related brain dynamics.

Evoked oscillatory cortical activity during acute pain: Probing brain in pain by transcranial magnetic stimulation combined with electroencephalogram.

Temporal dynamics of local cortical rhythms during acute pain remain largely unknown. The current study used a novel approach based on transcranial magnetic stimulation combined with electroencephalogram (TMS-EEG) to investigate evoked-oscillatory cortical activity during acute pain. Motor (M1) and dorsolateral prefrontal cortex (DLPFC) were probed by TMS, respectively, to record oscillatory power (event-related spectral perturbation and relative spectral power) and phase synchronization (inter-trial coherence) by 63 EEG channels during experimentally induced acute heat pain in 24 healthy participants. TMS-EEG was recorded before, during, and after noxious heat (acute pain condition) and non-noxious warm (Control condition), delivered in a randomized sequence. The main frequency bands (α, β1, and β2) of TMS-evoked potentials after M1 and DLPFC stimulation were recorded close to the TMS coil and remotely. Cold and heat pain thresholds were measured before TMS-EEG. Over M1, acute pain decreased α-band oscillatory power locally and α-band phase synchronization remotely in parietal-occipital clusters compared with non-noxious warm (all p < .05). The remote (parietal-occipital) decrease in α-band phase synchronization during acute pain correlated with the cold (p = .001) and heat pain thresholds (p = .023) and to local (M1) α-band oscillatory power decrease (p = .024). Over DLPFC, acute pain only decreased β1-band power locally compared with non-noxious warm (p = .015). Thus, evoked-oscillatory cortical activity to M1 stimulation is reduced by acute pain in central and parietal-occipital regions and correlated with pain sensitivity, in contrast to DLPFC, which had only local effects. This finding expands the significance of α and β band oscillations and may have relevance for pain therapies.

The influence of hyperchaoticity, synchronization, and Shannon entropy on the performance of a physical reservoir computer.

In this paper, we analyze the dynamic effect of a reservoir computer (RC) on its performance. Modified Kuramoto's coupled oscillators are used to model the RC, and synchronization, Lyapunov spectrum (and dimension), Shannon entropy, and the upper bound of the Kolmogorov-Sinai entropy are employed to characterize the dynamics of the RC. The performance of the RC is analyzed by reproducing the distribution of random, Gaussian, and quantum jumps series (shelved states) since a replica of the time evolution of a completely random series is not possible to generate. We demonstrate that hyperchaotic motion, moderate Shannon entropy, and a higher degree of synchronization of Kuramoto's oscillators lead to the best performance of the RC. Therefore, an appropriate balance of irregularity and order in the oscillator's dynamics leads to better performances.

The effect of nonlinear diffusive coupling on the synchronization of coupled oscillators

This paper examines the impact of nonlinear coupling on the synchronization of interconnected oscillators. Various powers of diffusive coupling are explored to introduce nonlinear effects, and the results are contrasted with those of linear diffusive coupling. The study employs three representative chaotic systems, namely, the Lorenz, Rössler, and Hindmarsh-Rose systems. Findings indicate that nonlinear couplings with power below one result in synchronization at lower coupling strengths. Additionally, the critical coupling strength reduces as the coupling power decreases. However, the synchronization region undergoes changes and becomes bounded. Conversely, for powers exceeding one, networks are either unable to synchronize or require higher coupling strengths compared to linear coupling.

Dissimilarity between synchronization processes on networks.

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a metric on a hypertorus, allowing us to compare the phases of coupled oscillators. In the first part, this formalism is implemented to examine systems of networked identical phase oscillators that evolve with the Kuramoto model. In particular, we analyze the effect of the weight of an edge in the synchronization of two oscillators, the introduction of new sets of edges in interacting cycles, the effect of bias in the couplings, and the addition of a link in a ring. We also compare the synchronization of nonisomorphic graphs with four nodes. Finally, we explore the dissimilarities generated when we contrast the Kuramoto model with its linear approximation for different random initial phases in deterministic and random networks. The approach introduced provides a general tool for comparing synchronization processes on networks, allowing us to understand the dynamics of a complex system as a consequence of the coupling structure and the processes that can occur in it.

Scenarios for the appearance of strange attractors in a model of three interacting microbubble contrast agents

We study nonlinear dynamics in a model of three interacting encapsulated gas bubbles in a liquid. The model is a system of three coupled nonlinear oscillators with an external periodic force. Such bubbles have numerous applications, for instance, they are used as contrast agents in ultrasound visualization. Certain types of bubbles oscillations may be beneficial or undesirable depending on a given application and, hence, the dependence of the regimes of bubbles oscillations on the control parameters is worth studying. We demonstrate that there is a wide variety of types of dynamics in the model by constructing a chart of dynamical regimes in the control parameters space. Here we focus on hyperchaotic attractors characterized by three positive Lyapunov exponents and strange attractors with one or two positive Lyapunov exponents possessing an additional zero Lyapunov exponent, which have not been observed previously in the context of bubbles oscillations. We also believe that we provide a first example of a hyperchaotic attractor with additional zero Lyapunov exponent. Furthermore, the mechanisms of the onset of these types of attractors are still not well studied. We identify two-parametric regions in the control parameter space where these hyperchaotic and chaotic attractors appear and study one-parametric routes leading to them. We associate the appearance of hyperchaotic attractors with three positive Lyapunov exponents with the inclusion of a periodic orbit with a three-dimensional unstable manifold, while the onset of chaotic oscillations with an additional zero Lyapunov exponent is connected to the partial synchronization of bubbles oscillations. We propose several underlying bifurcation mechanisms that explain the emergence of these regimes. We believe that these bifurcation scenarios are universal and can be observed in other systems of coupled oscillators.

Progressive Irreversible Proprioceptive Piezo2 Channelopathy-Induced Lost Forced Peripheral Oscillatory Synchronization to the Hippocampal Oscillator May Explain the Onset of Amyotrophic Lateral Sclerosis Pathomechanism.

Amyotrophic lateral sclerosis (ALS) is a mysterious lethal multisystem neurodegenerative disease that gradually leads to the progressive loss of motor neurons. A recent non-contact dying-back injury mechanism theory for ALS proposed that the primary damage is an acquired irreversible intrafusal proprioceptive terminal Piezo2 channelopathy with underlying genetic and environmental risk factors. Underpinning this is the theory that excessively prolonged proprioceptive mechanotransduction under allostasis may induce dysfunctionality in mitochondria, leading to Piezo2 channelopathy. This microinjury is suggested to provide one gateway from physiology to pathophysiology. The chronic, but not irreversible, form of this Piezo2 channelopathy is implicated in many diseases with unknown etiology. Dry eye disease is one of them where replenishing synthetic proteoglycans promote nerve regeneration. Syndecans, especially syndecan-3, are proposed as the first critical link in this hierarchical ordered depletory pathomechanism as proton-collecting/distributing antennas; hence, they may play a role in ALS pathomechanism onset. Even more importantly, the shedding or charge-altering variants of Syndecan-3 may contribute to the Piezo2 channelopathy-induced disruption of the Piezo2-initiated proton-based ultrafast long-range signaling through VGLUT1 and VGLUT2. Thus, these alterations may not only cause disruption to ultrafast signaling to the hippocampus in conscious proprioception, but could disrupt the ultrafast proprioceptive signaling feedback to the motoneurons. Correspondingly, an inert Piezo2-initiated proton-based ultrafast signaled proprioceptive skeletal system is coming to light that is suggested to be progressively lost in ALS. In addition, the lost functional link of the MyoD family of inhibitor proteins, as auxiliary subunits of Piezo2, may not only contribute to the theorized acquired Piezo2 channelopathy, but may explain how these microinjured ion channels evolve to be principal transcription activators.

Motor oscillations reveal new correlates of error processing in the human brain

It has been demonstrated that during motor responses, the activation of the motor cortical regions emerges in close association with the activation of the medial frontal cortex implicated with performance monitoring and cognitive control. The present study explored the oscillatory neurodynamics of response-related potentials during correct and error responses to test the hypothesis that such continuous communication would modify the characteristics of motor potentials during performance errors. Electroencephalogram (EEG) was recorded at 64 electrodes in a four-choice reaction task and response-related potentials (RRPs) of correct and error responses were analysed. Oscillatory RRP components at extended motor areas were analysed in the theta (3.5–7 Hz) and delta (1–3 Hz) frequency bands with respect to power, temporal synchronization (phase-locking factor, PLF), and spatial synchronization (phase-locking value, PLV). Major results demonstrated that motor oscillations differed between correct and error responses. Error-related changes (1) were frequency-specific, engaging delta and theta frequency bands, (2) emerged already before response production, and (3) had specific regional topographies at posterior sensorimotor and anterior (premotor and medial frontal) areas. Specifically, the connectedness of motor and sensorimotor areas contra-lateral to the response supported by delta networks was substantially reduced during errors. Also, there was an error-related suppression of the phase stability of delta and theta oscillations at these areas. This synchronization reduction was accompanied by increased temporal synchronization of motor theta oscillations at bi-lateral premotor regions and by two distinctive error-related effects at medial frontal regions: (1) a focused fronto-central enhancement of theta power and (2) a separable enhancement of the temporal synchronization of delta oscillations with a localized medial frontal focus. Together, these observations indicate that the electrophysiological signatures of performance errors are not limited to the medial frontal signals, but they also involve the dynamics of oscillatory motor networks at extended cortical regions generating the movement. Also, they provide a more detailed picture of the medial frontal processes activated in relation to error processing.

Forced synchronization of self-excited chaotic thermoacoustic oscillations

We experimentally investigate the forced synchronization of a self-excited chaotic thermoacoustic oscillator with two natural frequencies, $f_1$ and $f_2$ . On increasing the forcing amplitude, $\epsilon _f$ , at a fixed forcing frequency, $f_f$ , we find two different types of synchronization: (i) $f_f/f_1 = 1:1$ or $2:1$ chaos-destroying synchronization (CDS), and (ii) phase synchronization of chaos (PSC). En route to $1:1$ CDS, the system transitions from an unforced chaotic state ( ${\rm {CH}}_{1,2}$ ) to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ), then to a two-frequency quasiperiodic state where chaos is destroyed ( $\mathbb {T}^2_{2,f}$ ), and finally to a phase-locked period-1 state ( ${\rm {P1}}_f$ ). The route to $2:1$ CDS is similar, but the quasiperiodic state hosts a doubled torus $(2\mathbb {T}^2_{2,f})$ that transforms into a phase-locked period-2 orbit $({\rm {P2}}_f)$ when CDS occurs. En route to PSC, the system transitions to a forced chaotic state ( ${\rm {CH}}_{1,2,f}$ ) followed by a phase-locked chaotic state, where $f_1$ , $f_2$ and $f_f$ still coexist but their phase difference remains bounded. We find that the maximum reduction in thermoacoustic amplitude occurs near the onset of CDS, and that the critical $\epsilon _f$ required for the onset of CDS does not vary significantly with $f_f$ . We then use two unidirectionally coupled Anishchenko–Astakhov oscillators to phenomenologically model the experimental synchronization dynamics, including (i) the route to $1:1$ CDS, (ii) various phase dynamics, such as phase drifting, slipping and locking, and (iii) the thermoacoustic amplitude variations in the $f_f/f_1$ – $\epsilon _f$ plane. This study extends the applicability of open-loop control further to a chaotic thermoacoustic system, demonstrating (i) the feasibility of using an existing actuation strategy to weaken aperiodic thermoacoustic oscillations, and (ii) the possibility of developing new active suppression strategies based on both established and emerging methods of chaos control.

Prospects of cognitive-motor entrainment: an interdisciplinary review

Entrainment theory, a multidisciplinary concept referring to the automatic synchronization of oscillatory patterns, can be used to explain interactions across motor production, cognition, and environmental processing. This review summarizes findings from the three primary categories of naturally occurring neural entrainment: body-brain entrainment of involuntary self-produced rhythms, bottom-up entrainment between environmental stimuli and the brain, and top-down neural entrainment of self-produced processes. Studies evaluating entrainment's impact on cognition suggest that synchronized neural activation may alleviate cognitive constraints. Entrainment has also been therapeutically implemented to decrease motor production variation and enhance movement quality. When considering the evidence for entrainment's ability to decrease the attentional load of a task and increase cognitive or motor production quality, the oscillatory synchronization of a cognitive and motor task may be a promising technique that can be applied to dual-tasking. An emerging body of literature suggests that cognitive-motor entrainment may alleviate dual-task cost and, in some cases, lead to a higher quality of psychological and physiological task performance than when the same tasks are performed in isolation. We propose pathways for future research and emphasize the therapeutic relevance further experimentation on the topic of entrainment may provide. By understanding how to maximize neural entrainment's cognitive and motor benefits, scientists and practitioners may be able to harness its benefits to enhance learning and rehabilitative practices.

Modeling the interplay of oscillatory synchronization and aggregation via cell–cell adhesion

We present a model of systems of cells with intracellular oscillators (‘clocks’). This is motivated by examples from developmental biology and from the behavior of organisms on the threshold to multicellularity. Cells undergo random motion and adhere to each other. The adhesion strength between neighbors depends on their clock phases in addition to a constant baseline strength. The oscillators are linked via Kuramoto-type local interactions. The model is an advection-diffusion partial differential equation with nonlocal advection terms. We demonstrate that synchronized states correspond to Dirac-delta measure solutions of a weak version of the equation. To analyze the complex interplay of aggregation and synchronization, we then perform a linear stability analysis of the incoherent, spatially uniform state. This lets us classify possibly emerging patterns depending on model parameters. Combining these results with numerical simulations, we determine a range of possible far-from equilibrium patterns when baseline adhesion strength is zero: There is aggregation into separate synchronized clusters with or without global synchrony; global synchronization without aggregation; or unexpectedly a ‘phase wave’ pattern characterized by spatial gradients of clock phases. A 2D Lattice-Gas Cellular Automaton model confirms and illustrates these results.

Glycolytic oscillations under periodic drivings.

In many living organisms displaying circadian rhythms, the intake of energy often occurs in a periodic manner. Glycolysis is a prototypical biochemical reaction that exhibits a self-sustained oscillation under continuous injection of glucose. Here we study the effect of periodic injection of glucose on the glycolytic oscillation from a dynamical systems perspective. In particular, we employ Goldbeter's allosteric model of phosphofructokinase as a model system for glycolytic oscillations, and explore the effect of periodic substrate influx of varying frequencies and amplitudes by building the phase diagrams of Lyapunov exponents and oscillatory periods. When the frequency of driving is tuned around the harmonic and sub/super-harmonic conditions of the natural frequency, the system is entrained to a frequency-locked state, forming an entrainment band that broadens with an increasing amplitude of driving. On the other hand, if the amplitude is substantial, the system may transition, albeit infrequent, to a chaotic state which defies prediction of dynamical behaviour. Our study offers in-depth understandings into the controllability of glycolytic oscillation as well as explaining physical underpinnings that enable the synchronous oscillations among a dense population of cells.

Olfactory system structure and function in newly hatched and adult locusts

An important question in neuroscience is how sensory systems change as animals grow and interact with the environment. Exploring sensory systems in animals as they develop can reveal how networks of neurons process information as the neurons themselves grow and the needs of the animal change. Here we compared the structure and function of peripheral parts of the olfactory pathway in newly hatched and adult locusts. We found that populations of olfactory sensory neurons (OSNs) in hatchlings and adults responded with similar tunings to a panel of odors. The morphologies of local neurons (LNs) and projection neurons (PNs) in the antennal lobes (ALs) were very similar in both age groups, though they were smaller in hatchlings, they were proportional to overall brain size. The odor evoked responses of LNs and PNs were also very similar in both age groups, characterized by complex patterns of activity including oscillatory synchronization. Notably, in hatchlings, spontaneous and odor-evoked firing rates of PNs were lower, and LFP oscillations were lower in frequency, than in the adult. Hatchlings have smaller antennae with fewer OSNs; removing antennal segments from adults also reduced LFP oscillation frequency. Thus, consistent with earlier computational models, the developmental increase in frequency is due to increasing intensity of input to the oscillation circuitry. Overall, our results show that locusts hatch with a fully formed olfactory system that structurally and functionally matches that of the adult, despite its small size and lack of prior experience with olfactory stimuli.

Disinhibition Is an Essential Network Motif Coordinated by GABA Levels and GABA B Receptors.

Network dynamics are crucial for action and sensation. Changes in synaptic physiology lead to the reorganization of local microcircuits. Consequently, the functional state of the network impacts the output signal depending on the firing patterns of its units. Networks exhibit steady states in which neurons show various activities, producing many networks with diverse properties. Transitions between network states determine the output signal generated and its functional results. The temporal dynamics of excitation/inhibition allow a shift between states in an operational network. Therefore, a process capable of modulating the dynamics of excitation/inhibition may be functionally important. This process is known as disinhibition. In this review, we describe the effect of GABA levels and GABAB receptors on tonic inhibition, which causes changes (due to disinhibition) in network dynamics, leading to synchronous functional oscillations.

Synchronization of Analog-Discrete Chaotic Systems for Wireless Sensor Network Design

The current work is focused on studying the performance of the Pecora–Carroll synchronization technique to achieve synchronization between the analog and discrete chaos oscillators. The importance of this study is supported by the growing applications of chaotic systems for improving the security of data transmission in various communication layers, primarily on the physical layer. The hybrid analog-discrete approach of implementing chaos oscillators opens new possible communication schemes for wireless sensor network (WSN) applications. The analog implementation of chaos oscillators can benefit the simpler sensor node (SN) integration, while the discrete implementation can be used on the gateway. However, the core of such chaos-based communications is synchronizing analog and discrete chaos oscillators. This work studies two key parameters of analog-discrete chaotic synchronization: chaotic synchronization noise immunity and synchronization speed. The noise immunity study demonstrates the quality of synchronization at various noise levels, while the synchronization speed demonstrates how quickly the analog-discrete synchronization is achieved, along with how quickly the two systems diverge when synchronization is no longer present. The two studies use both simulation-based and hardware-based approaches. In the simulation case, the analog oscillator’s circuit is modeled in LTspice XVII, while in the hardware case, the circuit is implemented on the PCB. In both simulation and hardware studies, the discrete model of the oscillator is implemented in MATLAB R2023b. The studies are performed for two pairs of different chaos oscillators to widen the proposed approach application potential: the Vilnius and RC chaos oscillators. The oscillators have been selected due to their simplicity and similar dynamic behavior for model-based and electrical circuit implementation. The proposed approach also allows us to compare the synchronization of different oscillators in the analog-discrete implementation.

Ramping dynamics and theta oscillations reflect dissociable signatures during rule-guided human behavior

Contextual cues and prior evidence guide human goal-directed behavior. The neurophysiological mechanisms that implement contextual priors to guide subsequent actions in the human brain remain unclear. Using intracranial electroencephalography (iEEG), we demonstrate that increasing uncertainty introduces a shift from a purely oscillatory to a mixed processing regime with an additional ramping component. Oscillatory and ramping dynamics reflect dissociable signatures, which likely differentially contribute to the encoding and transfer of different cognitive variables in a cue-guided motor task. The results support the idea that prefrontal activity encodes rules and ensuing actions in distinct coding subspaces, while theta oscillations synchronize the prefrontal-motor network, possibly to guide action execution. Collectively, our results reveal how two key features of large-scale neural population activity, namely continuous ramping dynamics and oscillatory synchrony, jointly support rule-guided human behavior.

High-Gamma Activity Is Coupled to Low-Gamma Oscillations in Precentral Cortices and Modulates with Movement and Speech.

Planning and executing motor behaviors requires coordinated neural activity among multiple cortical and subcortical regions of the brain. Phase-amplitude coupling between the high-gamma band amplitude and the phase of low frequency oscillations (theta, alpha, beta) has been proposed to reflect neural communication, as has synchronization of low-gamma oscillations. However, coupling between low-gamma and high-gamma bands has not been investigated. Here, we measured phase-amplitude coupling between low- and high-gamma in monkeys performing a reaching task and in humans either performing finger-flexion or word-reading tasks. We found significant coupling between low-gamma phase and high-gamma amplitude in multiple sensorimotor and premotor cortices of both species during all tasks. This coupling modulated with the onset of movement. These findings suggest that interactions between the low and high gamma bands are markers of network dynamics related to movement and speech generation.

Development of the sleep-wake switch in rats during the P2-P21 early infancy period.

In early infancy, rats randomly alternate between the sleeping and waking states-from postnatal day 2-10 (P2-P10), sleep and wake bouts are both exponentially distributed with increasing means, while from P10-P21 sleep and wake bout means continue to increase, though there is a striking qualitative shift in the distribution of wake bouts from exponential to power law. The behavioral states of sleep and wakefulness correspond to the activity of sleep-active and wake-active neuronal brainstem populations, with reciprocal inhibition between the two ensuring that only one population is active at a time. The locus coeruleus (LC) forms a third component of this circuit that rises in prominence during the P10-P21 period, as experimental evidence shows that an as-of-yet undeciphered interaction of the LC with sleep-active and wake-active populations is responsible for the transformation of the wake bout distribution from exponential to power law. Interestingly, the LC undergoes remarkable physiological changes during the P10-P21 period-gap junctions within the LC are pruned and network-wide oscillatory synchrony declines and vanishes. In this work, we discuss a series of models of sleep-active, wake-active, and the LC populations, and we use these models to postulate the nature of the interaction between these three populations and how these interactions explain empirical observations of sleep and wake bout dynamics. We hypothesize a circuit in which there is reciprocal excitation between the LC and wake-active population with inhibition from the sleep-active population to the LC that suppresses the LC during sleep bouts. During the P2-P10 period, we argue that a noise-based switching mechanism between the sleep-active and wake-active populations provides a simple and natural way to account for exponential bout distributions, and that the locked oscillatory state of the LC prevents it from impacting bout distributions. From P10-P21, we use our models to postulate that, as the LC gradually shifts from a state of synchronized oscillations to a state of continuous firing, reciprocal excitation between the LC and the wake-active population is able to gradually transform the wake bout distribution from exponential to power law.